What's up good people and welcome to yet another episode of bars with stars right here on SPM bars guys if you have not yet subscribed please make sure you do because we have a lot of content planned for you now today i have a star right here with me someone who's been trending you know for the couple of the past couple of hours you know and this is none and okay guys this is none other than oliva otieno aka comedian why why hey looku see looku bro i'm by i dressed by me dressed by you um why why hey i bet you are ready for the wisdom today you guys you know why why yes people listen to your talks very much and you know they there is a net we see it yes and you seem to be a very wisdom with a wise person rata these are there we hosted you on our friends vibe yes what you follow comment section this is why why guy is very wise nini me experience is not experience and also acquiring knowledge in school acquiring nili on a jita futi asasawa kwenyei eh i read a lot of books i read a lot of articles okay infact must stay up all night i don't have to be reading uh from um a physical or an actual book because i have books i read a lot of books but must in asana kwa at least try to get information about this in fact this one information we're going to have for the longest time to mention to metafuta nani alitengu nesa in tanja to metafuta vilekina kwa moto sayo nani na toa na kuna magic kwa paipikiku yena pita kama ni moto sayi kiyo ayo kitu na shido shido nasi that is dangerous basi when you think about it ni metafuta juzy maka nime naka funguwe ni ni mita kwa isdanshawa waka aje but ita kuna ni metafuta akuna mutua mi explain si kula miseta explaini okitu atakula viusa po ita kwa presidencia candidate kumidians on atafuta shawa yume kwa aje moto hey why why you know that's actually something that crossed my mind the other day why did you call yourself why why that was my dad's name used to be his nickname yes so i took it from him yes niki yanza niki yanza nili kwa na naji ta kisiagi nili kwa na jyabi yangati ukiwa na jina fani kutakum fani jina kwa fani make sure everything about you is fani dress fani look fani and then atosipo chekesha watu akangili atu atu akangili atunguwe akua lafu wana unaitu kisiagi wana cheka hey watu aku cheka ezazote niki akuja niki jida triple o because i'm oliva utienu utiyambo so niki jida triple o it never worked so then i thought about nika sema can i be a little creative so niki na kuentafili niki ulizwa nitu ajina apinta kwa na sema kwa na sema tu atu i have abbreviated my name oh si juhini nia then i just went back nika juku ajina ya my late dad nika moku iru disha sasa to light na ion nili work by the way imagine probably that was the entire plan that was supposed to happen do ma na ulu kuno na true kumeni niki omokia nyuma ata wei apu nyuma maliuna oni apu nyuma bani niyo jina but elisha iyo siji shizo manizo 254 toh ayo jina bida you know names have very important meanings to people's lives nukweli nukweli sana yes utatwame jina yam toto wako because guys he's the latest dad in town and this is actually the first time i'm saying this the second name exclusive espiambas whoo drumroll she's called sise gaona hey sise gaona guys yes she's probably the only one in africa called that why sise gaona because i know the someone called that she's sise gaona first of all number one i don't even want her to get a son from me number one i want to cut the tribal code okay i don't want people to to ever know niwa tribe ganiu kumbele ehe epi aki anelia mbele aki zam toto to wachana naini ni tribal profiling so i'm killing that that is what deliberately na mombia si chuka ata yo jina aki chuka si kumeni aka manikinem sawa but kwa idea ke nata katua kuna jina very neutral sise gaona i like watching spanyola movies zam mexicano mada enyuma rero so rero so spanyora las so this is a character kwa movie na itwa falsa identitak she was a beautiful woman beautiful woman but mindset ya ke niyama naume watu aki na woma ali wanauma na kimbia but niya naba naba aki nika sema this is the name gaona yes that's a beautiful name hey congratulations yyy how does it feel to be a dad feels amazing it does feels great what has changed new level what has changed a lot has changed aha a lot a lot a lot a lot a lot asa hi masimu si shiki obi obi asa hi pasamoja si shiki simu ima jemili kwa ni kwa asika masana e na fa ni kwa na change daipaz ni ni na fa ni kwa na bond na mtoto yes skin to skin skin to skin ni ni ni so new life new things reasonings angu ni difference aii they got different ni baba na ni ima sa iziati hey by the way ni baba sise anyway ni baba sise abuata bifoto ndelen na mtoto back to the advice you know that you're giving because there's something else that you did yesterday you get what are some of the wife material traits you as a wife person yes think that every wife material every man that chooses someone a wife shh that wife should have those traits number one manamuke mani hafuri hee ulu ko uko ready na izivit mani hafuri e nkufura tu mefura tu mefura aaa wei wei watua hafuri for no reason aaa is women we will just wake up and then they all of a sudden they don't feel like coming to you nlambda unliko na ita mtu kandotum to minginae no let me tell you e a lot of women on da manya na po online e adio let a man not tell you anything oh let a let a no money should tell you anything e those that say that ah water single e single wala wa maybe they are single and happy wala wa praise your man so you need you cannot be single and happy but then uko ha the only person that can be single and happy is a man aaa now you know you've been because a man can be single and still enjoying fruits of labor come on we are single but we are single to who is asking you know badu tuko mambu etu na na tukama lakini tuko e mambu maweeli matata tuko na na wacha tu sendele apo ae wana mkambaya furi ha furi mmhmm nambatu nambatu submission e geto muna katai submission let me tell you some what is submission submission you know njwa sasa wana wacha uko ready for uko ready for no way why what is that no nambu ya as a host tia chasina mambu nambu ya nambu ya e a man and a woman yes can never be equal yeah okay women have to accept that mmhmm imambu ya what you call we atami miapa o kituna fanya niza fanya una rudi usiku usiku mibe na faka rudi usiku ee alakini nisi una eza rudi usiku napia mi na eza rudi usiku sendio yo suti rudi suti rudi hehehehe when the rudi rudi nika nawa uta rudi nina wengine uta rudi nina wale uko let me tell something yeah even if you paying for that house that's it is more to that house than just a house that's a kingdom that's a kingdom so we una lipa to rent kwa nyumba kadogo nyumba is just part of the kingdom kingdom ni kubua kingdom ni kudua nyumba tu ni kadogo kwa yu kingdom yote ee nyumba is just the so submission submission ni usiku usiku ee ee you cannot be you could okay no number one the moment let me tell you something yeah the moment you start fighting yes na mona ume amu uta iwen yeah that's number one let me tell you a lot of women the mistake wana me kingi ni kutume kata to sifil guilty for makosat na do just do your thing ok na fanya baya ukiri da liye tu ta kuna maliknae da ne nalewa nimi wana baya one two wrongs don't make a right yes the moment datini me kwa mili rudu usiku jana sasa ume rudu usiku ok ya now that's you newtoto sasa that's immature so kitu da fanya newta rudu usiku na hindi usiku ya kwa yamu isho uta kume siya ta kuru di tu uta kwa yu usiku ya kwa ta kuru ishiya uta ishiys yuma henda uta ume hindi apel a second chance let me tell you something the moment you start competing no uta kwa chance a real man gives chances to na pay opportunity baka kufiki apa si kwa na fika apa and you know men be one we will not just wake up and leave uta pa bianiaji ikitu na fanyaanga chunga sana oh da da da da nimi wacha sita iru dia tena muna poa muna poa, muna jifanyaanga muna sawo muna consequences li kwa karibu iku e tena muna sawo tena muru di pali pali tena ikitu nita yaa ii usiki kifikaanga mukiaji sasa muna anza oh hei ya li kwa na mutu all along oh si you ni ni men uta apiga matukiyo kama diamond venya lisa man apiga wa seno ake matukiyo akuna mama matukiyo if I will tell you something every woman that has dated me yaa knows how much over caring man I am loving but I don't take nonsense li no wana jo angafizu ni kwa ambia say ni sana na ne trafa tu tokihapa nifa ii kwa na wama nia aa a ni sana na ne tu na tokapa niki say ma ii jagi tole apa ii kwa apa wana zi no ii jagi kwa pa ii kwa uku ni kwa na sa ii uki maliza kwa unge ii jag kwa eka pale man ni lisa wewe kwa if you bidi afuana opinion kwa nyumba opinion akuna yo you don't understand ii isu si ni mi ni nimesemi ii jagi tolewe wona se me ii jagi tolewe si yola zongi mi kwa apa su unge ii weka pale si ni ii jagi angu ni mesema wona ni ii jagi si ni ii jagi angu ni me kubia na yo ni mesema ii jagi tolewe kwa so si tu ii jagi tolewe wewe kitambo su unge chuku ii weka pale yaa that makes sense you understand aya so when when you're doing your thing as a woman in most of the situation mi mi spenangi kuhu kuhu ingiliya vituza wana wake si ingiliya angi wacha fanya mamboa eka ni ni apuna kafridom tu kake pale kafridom tu kake kati freedom yaa asi danya tini freedom tu aya kuna kwa mene ii koregulete zena nisa tini freedom ganyu eni koregulete uka aya freedom ni hati ii freedom ukona yo usipo me isu kusawa e but utumi freedom weba ya e kwa zona jo wana waka na penda wana kwa mene baya sad mm wana waka na penda wana oh my darling where have you been I missed you baby girl how e hee hee wana subu wanga wana e wana subu wanga in Nairobi so lazima sazigi ni piya e as a man lazima utafeni yo frame yaa lazima jue e wu mu se anani penda nampenda anazandu ya anything lakini kuna extent ni kimi eka ita kwa mba hee wana waka so dem lazima jue extent ni akon they have to know the extent in which unawiza go wrong unezag viduza unezagu agil they have to know because if they not know they will always be testing your frames kila sikuwa na kufuta that is why wana je panagazila yutura so ni piyege so ni piyege let me tell first of all if you ever find yourself as a man demia kwa na fika na wei puntia so ni piyege so you have failed as a man because hajuikituna zafanya anafa skiza kwa na kikia uje se maa pii kwa tzindi uje se maa pii kwa bata nafa ajuie anawa eza tandi kwa lakini se tandi aza nafa tu anafa tu maa ni aja mi umuza aza tandi kwa lakini se azi wei tandi kwa lakini se tawa wei sasa feminis watage uzaikitu ni me sema asi tandi kwa lakini nafa ajuie aki jaribukuni piga miimi anawa wacha tu sendelen ewa story aya kuna demafuri kuna submission yes kuna kuna ni ni sasengina agiu meni kwa agiu aya kuna ni trust aya aya aya ati wei ni utunikiwa na mawa tu hangu unanya maza throughout I want somebody who will be a voice mwenyata kama siku na kama sayi kama siku for example na kitu me fanyika for example ata kofisi maali bibi anwa na fanya kazi anawa eza si mama kwa niyebe ofisi na seme our lawyers are looking into the matter so we ask you guys to be tia ti ulazi wale wa ni wakuenda wala na zima kwa mtu mene tia kwa modest ana so that one then we are talking about intelligence na zima uski e ana agiu aje in whichever the capacity the problem sometimes we judge people's intelligence based on the benchmarks that we have the problem is sasengina kwa relationship na demu niya kwa 19 and then na taku judge intelligence ya ke na Michelle Obama that's why we go wrong so kutabu judge intelligence ya ke judge na watu eni waku kwa levelia 19 years old twins and if you're dating somebody that is way younger than you as a man for example sometimes once in a while you have to go back to the area of emotion juna jwa uko 30 u sasengina kwa 20 most of the time there are a lot of differences when it comes to emotions okay so once in a while kuna bitu zene you might not be able to stand her sometimes intelligence sasu ama agiu niye ni so sometimes once in a while you leave your udume then you wu kbika totu kada but you don't stay there usi sindabu kikikikiki unapongidokiki so let's say if you know it is na fawzi kwe yes okay sawa accha tu sendelen isit traits juna juo niha di kakwa Nataka kusahatu sata muna kuja kukula chips because most of the situation i'm not saying all So during that situation they'll generally say they will not be able to pick a child. And it isn't her fault and if it is not her fault mwana to pick a child She's going to ruin her because cooking is a basic need not even for both men and women cooking is a basic need but as lots are providing, cooking can be related for sure kama wuna provide nice QA nipprovite na alabda na nikuji kupika nipprovite minit funikiyu mi na funikiyu wana kuji wana kula bade gopone the man of the house kuna kitugini waga abad kupika so i'm telling you about your bringing up the way it affects kwa na dem haju kupika kuna kitu mamaa ke akumonyesha na kama mamaa ke akumonyesha kitu kama iyo basi chances are kuna bitum mingi aja onyesho apart from kupika so we can notice cooking is a vice then you have to scrutinize again other things kwa zudapata uta kuwa wana ishina mutua ko 30 na alabda kuna aspekta za life za ke zengya hazija maturishwa for example umepata weo dem a kuna everything good kila kitu yuko poa as in intelligence,submission kila kitu lakini weo dem abeendi kupika ni iyo tu kupika weo nneka ex juya chakula iyo tu siku i will find out i have to be logical as a man what makes a man is logic la zima uju ni kwanini haju i kupika na kama haju kupika i will have to scrutinize other attributes that are related to kupika kama kama nini wana iyo ikina kwa naka kichuongumu maali dem wana iyu tu kupika chances are kuna kichuongumu kwa touch to it imagine you saw between zengina zote zikosa hiwazi it can be perfect hiwazi these are attributes every attribute depends on another hiwazi pata tii atimana wama nne aja ishika 10k maisha ake kuna gari atu semi a tii aja wa ishika pata kuna gari awezi la zima ushika iyo 10k siku waja ushika 20, ushika 30 you can say that kuna nneka ishika 10k maisha ake kuna but imagine you saw between zengina wana wama nne ni mhad working lakini aki mazin do badu ni kama nyotaki dogo ni uta ake mazin do badu ni mkata lakini wana he has a very great vision sosa wana wame kama utifanya nawa unimi wana juwa nini muna ngalianga wana wana ngalianga vision wana wame where is your vision no, main nikonayo but you see I want someone that can compliment me can you look at your vision no, I want someone that can compliment my vision because I have mine but I do not want someone that is going to set me back yes you understand that's where I'm coming from so nini makosa wana kwa nga nazo nia bia wewama wana wame utifanya nia iwa iwa wana wama nia kuna vision akuna vision lakini doki dogo imemkata but wana nika ma ita kama nama one thing that you have to look from a man nama one is integrity ok how integral is this man aki kuwambia ako town nana kwa nga ako town nene unona because if kama kuna kitu inafanya nga what will grow kwa maisha in all aspects is integrity umsem transparent you say what's official kuna nga maluna nga nia wale wu mempea kazi kidogo amenda kuna na pesa wakuna ma vitu nani what to do kina nani businessman of Nairobi kina na real businessman are very disciplined they wake up at the right time they go to the office at the right time na uta aipata unana wana wana nga wana aona nini wana spend 300,000 na business man wana fanya ile legit ile seeo legit ile aonda ile real businessman na pata na spend 300,000 wana sitting ile pata na labda bieshara zake zina mleta 250,000 na day so anapil ni kama I have wasted this day so anapil kama so anapil kama yes yes yes so a serious person you will never find a serious person when you are extravagant extremely extravagant you will never find for sure I think actually that's very true girls mess kia those are some of the things you should check kukia wana mtua mea kwa so much extravagant kwa kwa kwa kwa kwa muna kula kula sayo kwa kwa kwa kwa kula sayo but anyway you guys make sure you subscribe to SPM Buzz aya imesha ii kama 20 20 la sasa so beti je uli zekwa ni a average women havarigli looking women ama ma dem 2 wana kama ni kama ni wana average ama ma sumaya wana kama ni kama ni wana average why they so happy in relationships muna wale wana te seka wana te seka ni eida wale sura ile ingina kabi sa ama extreme how average yes why because of your egos sasa wata uremosa ni amla wata uremosa yubaya uremosa yubaya nukipata demrembo manya ako kwa relationship and they are very happy afani zovitumuna utakanga wafanya amesha meet amesha meet let me tell you something do you know why a man will leave his house in kileleshwa or ronda kileleshwa ata meisha atas yukani metaja kileleshwa ja main atuako kwa nikila kileleshwa kileleshwa ma demo miaribu kileleshwa ma demo sita wana nakuishi wanyumba 60,000 3 bedrooms 2 wawili wana inaka each bed per sharing 10,000 per sharing wana isi kama wata waka vacation wana kwa wata wana pelekua air bnb wana kwa ni kama waka air bnb so why would a man leave his wife nalana house help you want to blame it on the wife? no please thank you no because not the wife but kuna kidwenya wu hasi wana ayo ati hausa nini piya amesha kanga piya nini akshe mtu akulala na house help waiwai atalala na air yata wafanya ni sawa that's logical mtu akulala piya ata ukwenya atalala atalala tu but sawa but in situations respect kwanza skiza so nga nga ni mimi nga nga nga wana but I'm telling you why some of them might do that I'm just giving you an example submission is a turn on to us than the ati for example mi nawe tu me agyu ni magyu na dem and then ati ananda puti because silent treatment it does not turn me on as a man every time nafil ni kama tu me agyu na dem alafu ame nga sija ame fanya ni ni ata labdame nga sija alafu ajaribu kufanya ni ni ni ni happen what is the problem can we talk about things it makes me even don't know this there's nothing as good as there are two words in the news na kwa ga very nice can we talk about it let's have a conversation about it wana so the problem ni ati dem ame kukusia ame fanya mako but then you need to kusia sa na sija mako sa him tu na fanya nga ni nga pi wana kusia wana kukusia mako zana fanya nga ni nga pi nga pi iyo kuchatnawe na na chatnawe iyo ni mako zana fanya nga tu where do you know iyo nga ni bigi everything but anyway I'm just kidding away from that any time as a woman you're silent on your husband ati you're quiet ati na nene the devil will talk to him shetanya tamonga lesha mami sasa wewe unanya maziwa apa na kuna mutu pala rohizambu na hawa rohizambu wana pika chai wana riyungo alafi na heko maziwa maji pumali maji tanga weli alafi hey hola masada nolizwa tanga wezi do you want coffee o do you want nene unaka majimoto unaka majimoto ya kuga na kuna hotsewa but that's for you by then maybe I do not support silent treatment because I believe communication is the most important aspect in our relationship and if there is no communication then what are we doing there is very tiny nothing we are doing but anyway guys okay that's a good one now yesterday why ume kuna hepa isoriyangu sada so how are you doing yesterday you posted a beautiful woman a queen a queen and the queen was not just alone the queen was expectant yes why ume amo uta to release even if it took my KCSE results because for the longest time I've been quiet how come na muka dani simba amenyesheo muka dani uko pekiako muka dani simba amenyesheo na iyo piya ili iwefunzo kuwa wat? iwefunzo ike waiwai uko na kiburi iwefunzo na iya piya tunasef tu standardun na kaka dem tu piya murembu diyo siyambia watu oh that good looking women diyo ono na iwa kwa zile attribute zote za uki taku datimutu and sure they are good looking to you and sure you find them sexually attractive the moment you don't find your woman sexually attractive apu katikati muna na kwa chana kwa ni ni zote infakti ni one of the key points la zima she has to be sexually attractive to you to you if you don't find your woman sexually attractive live today today today tukasai unena kumuwacha unena kumuwacha even your man is not kwa kwa kwa kumuwacha but you will cheat you will cheat because you will go looking for return so also that's not all those don't mean that men are perfect ono na piya ni wa kora tu wa kora tu wa pa henge wa mese mbuana lakini fili sisa mimi ono na yonu eno na fuku ono na ongelea mimi na fani kue na sema shidazenu shidazenia zina pa anya to fanya mambo biletu na pa anya but lakini nini na umu na kongo mekaliya hapinesi eno emu imagina si atu kwe tu musa mi si ati ati, ati, ati, ati, imaji niya ni niyo tu imaji niyo tu ala profisyon zip na provide imaji niya ati si tu tafta pesa nini niyo tu ati nini ni kujilea na tu sema tu niya chiaya ko sii miyangu kiliata kamin demu niya na pi kuna na shikana later niya mambo ya kui shikiya sii ju api you know where the problem comes in apu kwa submission you know because now the world has changed everyone is working everyone is bringing income in the family so I feel sometimes women feel like you know you're still expecting me to submit 100% but again I'm bringing I'm helping you provide but when a man provides by the way naka mamchu anaku provide niya na usubmitu na kusiasana now you issue ya women feeling kus madem skizu wako zileza ati a modern woman namu niya nga demu niya nga tweet kwa tuza modern woman now seju ninsu ni nuna padan demu tu akushina kwa kelabo so when you modern gani modern ghost modern gani so what happens is that it takes a lot of humility niya from a woman that has money to submit to a man check very well ok nalia mademu wengi wana ju atama icons wengi wana ju wana kwa nga doi kenya chasa sahara anamutu niya and it's not ati juma na ume ana it's because dema kwa na pesa yo pesa kwa tata dashi daga tu apu mutu kwa na dukit wevo the way I'm providing mutu wengi wana dukit daga sisi you provide maisha tu yote mademu ometu chiti maisha tu zote tu mai post mai honor to keep post oh women are dogs si you need aa kerji besta ya kwa si ame post bibi ya kia wu you see mana ume mwenze tu let's talk about men please let's talk about men mana ume maupen aa no sasa umenza kwa tena 180 races mana ume maupen mana ume maupen mana ume maupen jampatin mana ume maupen no what we call this person mana ume maupen why no pinigadam fukisunzi ya bugda anyway yes sasa kereji is just not one of us ay in a polite way eta ni ni mukini ni una lakin ule dema lady serve bida if you look at the things because ule dema li kwa piana vuga social media so I feel like with our audience pier kerji had to come out to jere bukukiliya nemi ya ke wu imagine ume nun liya dem ahudi ea ume ume kama isya na isya kereji wana manyumakada na nezake muna wana aneza mumu isiku e inyubai wiki e kikwana leakage kidogo sijui tap majime isya kidoga kipampampu ngeba inyubai ini muna lalauku kama atrapo vacation ala usasa wewe ona kembia sijui nenda kuchit sijuku fanya ni ni ala funa anza kutangaza online my friend iyo gari to try kujia kereji a li kujia li chua gari tulifura isa na kama ana ume a li to represent so hapo a li a li bonga points a li nyo apu ma liya unge unge a mingi ala utena tukona rizuna wana unge a bonga points se kapanda wela li chua gari we a li tuluku atu mefunga yukesisa sa bonga points se ma liza waza kereji nitu izikando so besema kereji ndo chiya manu a men's konfrensi mua kaka a zistar mana insekretari manzisha na chiya man nirektrum trust bado tumunini kidogo tu wana kidogo baka atayenda baka tukima wana na kereji baka together usiguni ni a wai wai ritu atu a Rudiana muna a chana 6 months muna a chana 4 what muna a chana 4 what kama muli a chana 6 months nini juya rizun muta a chana 10 na funga chapter move on don't be desperate official maria official Maya lovely official Maya Maya ume sema kuliti zote zeni ume to ambiya Maya akona zote baka mingi zaidi kusinda iso ni gani zengine ziongeze ni gani actually what is that one thing that made you at decide this one is the one that I want to be the mother of my child new submission okay new submission Maya na jovizuri mimi suweze mochapa suwezi fanya nini suwezi nini lakini kuna bichu zeni ziki fanyikanga usiki anga oliva penangi yo yo oliva kipata eh saini sa maoja eh niki kainje sita muchapa but noona kuna boundary sa me but you know I feel some things new out of respect out of respect respect some level of respect zegi nimi ata niki toka kuangu nesiki niki kama I'm stepping out niki kama awote ni ma wana wakia wana ume wana wakia 2 puawa niki kama 2 noona number 2 which is also important that is about her but which is also important to other men hygiene yes uke kuwana wana muke moja nacha chupa ya soda kwa mali TV na ekuwa nacha wikombi apu muna kana viyombu 2 days remote ina anguka wooo wana wana wana wana wana zafanya tabi asyara awezi mutasumbuana so yo ni uke kuja kuwana mukuna chakula throughout wageni wana tersemusha number 3 ??? uke ??? kwa naenda skwezi wewa, owa da disappointing people there at night waku disappointing wa disappoint chu lakini wale wa kuni ni, wale mbu gurunao na ni ni lasima ato wa kujapwa nyu mba kidogo wana, wana nali wa kitu ato wa wana onje kitu wakule wa fanya ni wa buru dike isi kuya tii, oh now days you're just chilling with your friends oh so you now days you're just doing it with your friends oma beshizakwa kujapwa, mista ki kwa na na ni the moment you lift your mouth and say that steak ki kwa na na ni wewa na tuwa na kwa na ni lakini wewa na nita kwa meona tabiaza oh yo rafiaza ah meona pa ni missi yo ni kwa ni tabiaza iso tabiaza na mafek apana iso tabiaza kwa ma ni mekwa na iso tabiaza ni kakupata waja kwa ma ni mekwa na iso tabiaza ni kakupata ni mekwa na ina ita tabiaza ni kakupata kwa iwa na manisha kwa ma singe kwa na ei singe kuni ni labda tabiaza ki atu jawa na ta kuhin flense bada kwa na ni kwa mbujue kazi women ono no huya rafiki wewa na nasema utaki ali saye na maali ni waka inga waka kubali na kitaka wewa na uta ena wewa na hichar wewa na hichar anafaya na anakaya kamaati basu na kamaati siku na kani huyo na zi mumu isi mukishi na de staki na ni na nansikuja ni apa wewa ni uta ni ni aki ukiske wu mewa chatu na tuwa japewa rezo nuju ni kamaati kamaati na faja na ni ni mzuri ukia na tuwa beshizaka olawa saden ukoni yukuwa relationship alafu ame kuja tukuku olawa sadeni waka watatu ame kuja kukulaku waka awja kuja waka na nandja infato ali wami shiba mbaya wami kuja auditions na ni auditions wama na ume nafa kuja kama shiba if I'm coming to audition my women's my friends women na zi mani kuja kama ni me shiba wana jetu? niyo hichi ya kule kwe tamu mbaka ni fanya mimi na ni me shiba ni taki kwe kula junaza kuja ni seme ja kuja tamu kuma ni njia na ni njia na zi mani kuja ni seme hei chakula ni tamu kuma ni njia ina ni ma liza so na zi mani shibe aaaaaa hichi ya kule ni tamu wana waiwai jama ni e anyway tawa you know now you mentioned something about age and looking at Maya na wewe suji kama there is a huge big difference na kama iko 12 zi kwa zi waduku me mention if someone is younger than you there is a sometimes you have to do something something you know just to be there lafu unato kachaluna do this tell us how what's the age difference between you and Maya around 7 to 8 wow okay 7 to 8 that's quite a lot yeah it's not a lot it's standard that's a standard standard not it marika wana subuaga wana na seza ni kama ni ni njia seza tulizalia wa sem ni ni we ni innu kwe li and another thing ye e I'm not saying that it's wrong to date somebody that is older if I have ever dated a younger woman in older than me oh ye how many years oh a lot as well seme yo in k mulisha upi 10 8 8 years us kribisa nikiaster Aga kuna kuna kuna kaos, tenaktafta malini kienda, kuna kuna kuna kuna. So there's an egg difference, which is also very helpful for her, especially even for mentorship, because there are things I've seen that she has not seen. So sometimes the reverse in a kwa nga rong sana, in a kwa nga baya kama dem ni moulda, na wewa simu waes kama wana ume, ama uja machua kama wana ume. It's likely to affect you because this woman has seen a lot that you have not seen and so most of the time she'll find herself in a position whereby she wants to mentor you.  When she starts cooling you, she feels like an adetum doi, but if you're younger than the woman, but in every toziko kwa hi kichwa, anafili kama wendo badunam skul, then... That would be tick. So guardian is top notch. Tick, let them have a good time, let them enjoy themselves. You only live once. So it's very helpful, our age gap is very helpful because also inampechansi yaku, yaku grow towards me. That's why na kwa me asadini na na toka from my area of emotion and then I move to her area of emotion and then I go back, I don't stay there. Si shindangi uko kwa ni. Na shindangu ni kitafutani kwa nga baya kwa ni na lafuna rudu kwa area of emotion kwa mi shindaji. I really man does not become romantic throughout. No, no, no. You have to know. Ramazinia kusyotu ya relevance ya una exist. Umi shindaji, una fanyani, una takani ni ni. Tu endani ni ni. Have a good time. Bitu shindi apu. Uki shindai apataku darao, tatafutau le manye. Because women are wired to be attracted to those that they perceive are of higher values than them. So anytime una shindanga uki submit, kwa wendo, kwa dem baby sasuna takaji, babies tu fanyaji, le fanyaji, ataku acha. In real sense, Bado ma dem una semanga aondo wana ume Bado wana taka waku apena. So you need to know, he is loving me too much. Una yanyi bia mujiwa ni kitumataka. He loves me too much. Yana ni pigiwa sasote. Sayana famu pigiwa sasote. Eh, wewa wonezutaka uku pigiwa kilawakati. Tenna, si pupiga sasote. Sasa, pigi. Sasa, ok, wonezutaka uku pigiwa kilawakati. Muna seba muna sumbulewa. But sasa, wonezutaka wonezutaka ni. Wonezutaka Bado. Wonezutaka a cocktail of. A kuwe mizuri na Bado, a kuwe maharo ngandi kido kwa. Wonezutaka, we want everything cocktail kido kwa kwenbali. You we cannot find utapata kichu angumu straight. Just be more desperate. Ama wewa. Wooo. Wonezutaka wonezutaka wonezutaka wonezutaka wonezutaka. Uza, wonezutaka wonezutaka wonezutaka. Uza, wonezutaka wonezutaka wonezutaka wonezutaka. Uza, wonezutaka wonezutaka wonezutaka. Uza, wonezutaka wonezutaka wonezutaka. So, wewa, wewa. You've now had an experience of dating someone who's younger and someone who's older. Yes. What is the difference? The difference is actually relative based on what you're looking for from a woman. When you're dating an older woman, you're dating somebody experienced. So, the fights that she picks up with you are so much different from the fights that a 21-year-old 1918 will pick up with you. Kuna fights asya pigana na zoma kama wona easy vitas easy change. The aspects that manoma ikama iiha easy change. So, it's not like that.  So, he hadjui ni ni ni, he working ni ni. So, wewa 19 na working na, vile na taka. Ula mungirana working na, what really works. So, that's the difference. So, as a man, you need to know how to balance between who you may na work na vile na taka na who you are vile, issue zinafa ziku. So, the probably challenge also comes when the major challenge sometimes when you're dating a woman that is older than you is differences in your faces, the life, and the things you believe in and the things that you want to do. Your goals might be totally different.  Ya watoto. Wesandewa na taka watoto. Ono na. Na iiho ni, number one thing in yana fanyanga, watua kusana. So, when a woman is dating someone is to marry them, then one day we can have children. Unless I do not want it prior, ni me discuss prior, I don't have a problem with it. So, can we just get married and stay? Then it's okay. But then on the day as a man, I want to at least have children with you. I love you at least. I want to see evidence of the love that we have together. So, difference in goals in affecting yana, because when you say, wucha li, baranda ku pati, baranda ku ruka ruka, baranda ku enakulaba fanyanga.  Wewa baranda ku invest, wewa baranda naji yambia. Ah, shere nashikawapi, nabaya ni ni. So, you will never go at, ni ni. So, one of you has to, in any relationship, one has to sacrifice themselves, or an attribute, or an aspect of themself. Ono na kama mi ni kama na ume? Ni kama ku compromise. Ya. Kama mi na taku pati. Bado. Ni kofesia ku pati. And you as a woman, kikue li kue li, u li siya pati.  You should compromise, u join here, mi mi li enjoy. So, kumini matia ruke towards me, mi unfair. Ya. So, you let them party, then what do you do? You join them in their area of interest. Ya. So, then you find a common ground within there. Yes, within their interest. Within. Yes. But also now, again, I realize, u li siya pati. So, isi kwa extent kubua. Yes. So, piya make, kak compromise. Yes. That works. That would work really. Another challenge in a kuwanga, ya, dating in all the woman is here saying. What are people saying? Ya. What are your friends telling you? Oh, it affects. It does. Big time. Really? Oh, big time. Nimi ono ajiwa bati na Diana, they've been intact this whole time. But, but it's a pattern. Yes. But, ni amang the few. Ya. But amang the few. Kue li. I don't know. I don't know. Naa, I don't know, ya, naa, ya, naa, ya, ah, ah, naa. I don't know what it is. Aa. Su, aa, aa. Aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, Yes. wata niche kelewa na deti mutumu dogo wata niche kelewa na deti mutumu zesawa I'm used to that but muta kwa mbe una juhu na naku chekelewa wana ni tenu kachinu jambe eh wana na naku chekelewa so you start looking at all yanga women again wana jebe eh ama nafani achi ulewa wango ama simu attractive ama simu ni nini nambath three or four nene lishupi nina ribingi lishupi nene dem older na ni na yes na chalim dogo insecurity the older woman anna jam kwa mindi ake however beautiful she might look kwa mindi ake de jambe eh I'm not sure kama ni mumichu I know kwa tunawatu ama unangwa jatusi kufu lani wuki fika 35 ama wuki fika nini uta ndi ama wengina will you will you so as long as there is this doubts as long as a woman has doubts they will always fill those doubts with the option jambe eh ama ni ni kama ake pata chansia kufu flat dungi na ta flat dungi na jambe eh and then of the day nene watua kujaw mambie eh mimi nili adeit mitu miang hee ni unize wana zanga visuri wana zanga su na kumukana ni sini wupi cha ake na ni wana zanga visuri wuki fika nini anna kusika trena dema kufika home so every day you will find yourself if you have she has not made her her mind completely dungi na pikanatu de li every day unasiki akuwa nana jwa dema dema ma ma ma ma ma ma ma ma ma ki dita chingi hata kama jya konga lisha bata kama na kwa nisha every day you will feel it then as a knee stick na kwa miaga hatu kusawa hata yemoji na dry hee ameni ambe I love you ameni ambe I love you ya L-U F-O-L-O-V ameni ambe I love you L-U-V ameni ambe I love you naku you aka eka you nama zama love ya hee apu kuna shida apu kuna kuna shida so it's just like that so anytime kuna kunga na gaps kama iso demu try kui feel and they can't feel it with you they don't think that run of high feeler discuss na hata try kui feel wapi ma li anyata feel kama ako igwe ake na kwa supplemented wwe kuna mtu ali zema iso mambo zote zote they don't matter it narrows down to money shida ni umaskini kama kijana ni mdogo ana pesa wewata watcha to leki ni kama ako na pesa na Juliza is this the same case with Bahati so ni guliza suali Bahati ako na pesa hae ni guliza ni guliza suali na ni na ni na ni kwa na ni doktor dress ome divorce na ni bilo ne so pesa ikwa api apu ayu sasa ulam bilo kuna shida zingini no in terms of age when it comes to age and when it comes to the difference in age so sasa iso witu zote ato wiki ambiwa wambiwa witu ati chali ako ata kwa chani ni na ako na pesa uto wiki ako let me tell you why it's not money just that money creates an attribute or a characteristic in women it's not the money but it's a specific attribute ni na kujanga but money is part of the thing nini na fanyanga dem nili kwa mbianga anupakanga kwa kwa feel ni kama you are of a higher value higher value in most situation ni bile ii me attachu na finances it's not necessarily finances for sure it's either finance or emotional na jokuna wale reya na mkushina na pesa after na mkushina na emotions na na mkushina na pesa after na wewa sasa ni ni ni aki wose so wura pesa wewa wose ni you are not taking a ground so u dem na feel ni kama there's not any aspects of leadership in you akuna kitu na impact na akuna uwa na ume ni una letter uwa na ume has so many things number one emotions number one care and number two care and provision ono na so easy for you kama haziko kuna wene dem aki feeling kama na feel voidiake kwa meshake ataka mauna do ataka how many situations kama tii kuna devlana kwa na do bata ma kwa ma na ki boi fula ni apo kusu boi kuna voidi na feel de ni ni ha muju kama kuna villana treats isia tu juia tu oni e so sometimes what happens is that wewa wuna tu do is a coincidence to a wuna do sendio but wewa pia sin duume so ame kuwaja usin duume but sasa wuna kelea pe desa ame ni waja juina pesa ni kwa na pesa singe ni a lot of people wana achuanga na iso pesa za wama yo pesa hako badum pera lo di kuchi kuchi to doemi now you know i really want to know how did it feel waka tuli ambiwa you having a baby mai alikuja kakwambia totoa ma muli kuwa pamoja mkaenda husi you know i just want to understand you know your fans also want to know alikuja kelea alikuja kelea prover fi kelea ta say ma na excetum toto ni muambia wa nani wa nani wa nani mi mi na wewa for the last six months tumela na pamoja tumela na pamoja wana nani wana nani so maybe she was thinking about that and also because it was her first time so alikuja kelea I think pregnant ya is that the reason to cry no it's the same thing it's the same thing hey hey she's lucky bana watu wana bengwati nani nani tu na juana watu wana ruko okuja bro dem wana ni ruka hei dem alikuja finii ambiya kuna mimba hei niku wami ya akadebia no yols mimi mi nudubi mada tayang h okuja wibu ni miku dafora nikuwe mama niziae ke raka ni ni ni ni ni ni ni ni gyauzwa so this one happened like that or super excited but we just wanted to be sure so we bought a lot of test kits kata kafanya kafanya nami fi aemi kawma nika test na yurini-yang Niwe. Oh, it's a legitce. Jiki leta niko nami mma. D'nda narsia nami mba wasi ni false positive. kisha mmbaya. Todd watia waiweya uiiyo nake. Ni liya una. Ok, before 30 so have we expected you to see her marriage ama what's going on in him and we couldn't attacked her In this world ne god tu unfold Yes I might speak here then my words are used again is to me please say my oh, the one who used to be walking next to us But today We were going to go get some tiktok and she said I will marry her but then she got the post saying you will go世 We just believed that If it's a good thing, God says It's the right thing to do if you are in the right place, God will guide you naka maa hapo siyo maalina Fani kwe and it's two if it's two, it's two and if it's two, it's two That's the thing So how long have you kept this relationship private? Because in 2018, you said you had a heart breaking in a normal, but you didn't get to know her. Yes, it was 2016. Yes, it was 2016. So how long have you guys been in hiding? 2 years. Ah, okay. That's really good. 2 years. Alright, let's hear. 2 years. I don't know what you said, but you said you had a comment section. Yes, I did. Yes, I did. Yes, I did. Aki jamani. One and two me are congratulations drivers. Yes. Okay, so how long have you guys been in hiding? Congratulations. Congratulations. What do you have to tell them? Congratulations. So the ones that are disappointed maybe they, you know, they were looking at you and they were like, this is a potential comment, pal, what are you going to say? Let's keep on being friends. I have a lot of baggage right now. I have a lot of baggage right now. Yeah. But anyway, you know, it's, they kept quiet. Yeah. So I've always been there. Yeah. I've always been there. Yeah. I've been single for the longest time. Yeah. So have me kwaengatu. Yeah. So say you need kusha, butter, kitu, kali, and you just as a, You are disappointed, you are disappointed, but I'm not saying, now I have a DM here, that's just two me will kasaema kitu. Yeah. So they kept quiet. The problem with these women, they don't want to shoot their shots. Yeah. If they shoot shots here, the reason I'm not finding is the shot. Yeah. Nisa zi gina tu ni labda. Nila, but actually, Ita ingiya tu. Ita ingiya. Uki shuutshotu na josu ita ingiya nga puti nga on na. Uni ulua kuhuze. Uni ulua anini. Anafajaji uyu nini. So wali wali shuutshots. Kuna niya piwali funguatu rawa bide. Namunia niya beba kandaka tutugu na watotu ziunini. Kafunguwa rawa na nini. So a lot of them have been showing me love. And some of them are telling me I'm a broken butt. But anyway I'll still support. So if you love a flower, if it comes back. It was meant to be yours. Why? I read somewhere. Sasa wacha ni kushike. Yu kukwam tandao nyu wa same tandem taona. Well, why Sades? The reason he was single that particular time is because he does not believe in sex before marriage.  Na sasa umeni ambiya bado amjawana. What's going on? Did you change your mind? Niki sayema jana ni me shibaso nisi kulele. Agwebo li change minds. Niki sayema sasa jana ni me konanja utanda umeni ambiya. Ukuli li konanja jana. Nima tuki ogani li happen. Nini ni li happen uka change minds. I just decided to reward good behavior. You reward good behavior. We don't just sleep with any woman. If mimi kama ni ni meila nawewe. I was rewarding your good behavior. You deserve. Wai, wai. Mtoto na fungulia page kuwa Instagram. Wai, wai. Agu muiki kukwam tandao. Wai, wai. Uyo si. Nafugwia ni nyama. Uyo si. Nangia lafina jiji bwapu kama nila wamilamwa. Atibuda nila wakufain nila fu. Konki. Niliwana maya jana liandei kaka komenta kasiima our daughters twin. So that means you look the same as the baby girl. Wai, na nga jua kuone isopicha. Niki. Kini. Ami piga kuktegil. Yungu na rembu ama maki. Ika tewa ki tujimona jo sasa boy handsome Iki ni ni ni apua lafu yu mi Eh shi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi yi Ika ule sasa nde omo toto wa Instagram model But tutu amoe ka uko Tukufungu li account Because at the end of the day that is Tutu akwa na danganiana because I have a funny content Erisista angona fanyakonten so hey page ni yaa ke So kwa amutu ta fanyakonten a man say hey page ni yaa kubado It is me still posting there every day. Thank you daddy, I love you daddy. It's a lot of work, but I love you daddy. So ni kama mingela jpenda. Yo ni kakupiga mukono wa. As we finish, please tell people, what are we expecting from the newest dad in town? From the newest dad in town, what are you expecting? You're expecting another solid man, when you append Yupuze. Uge kuja na uji inga apu kwa peji hangu. Tu na kutafutas, this is, tu na kutafutas, tu na jomali kutakupata. We have legal channels that kutafutas, na ngoto tu na kupiga propa. Ya tu ni mi? Oh ni mi, oh sii ni premium tiers, kwa sii na premium tiers apu. Na kutafutas tu na isu premium tiers, oh do takunyo isu premium tiers. Tu na kutafutia premium tiers kuwa, no, no takunyo. But anyway, we expecting a role model as well. Okay. Na ju sayo na takun taftasana. Chains to behavior. Sayo na takun taftasana. Pwale kuwa, kwa na takun taftasana, kwa ni kuwa na clients, tu na kutafutasana, pika pika pika. Pwale kwa team master tu na kungoja. Mi na zahomba tu viviani. Mupige tu akun na kitu mutani fanya. Hey, sawa basi, tu meskia waiwai. All right guys, thank you so much for talking to us. Tu na ju na Rudi kushugulikiam, tu tu you miss the baby. Appreciate. But thank you so much. Now, we have something. Baby atami travel, alpana na dege. Eish, we are sorry now. Now, waiwai, we have a gift for the baby. Tu na takun na ju Riyaia wa mejeparnga. Kido uile, ni ni ya uaiwai tu lehte, So, something. We have, things ready Bana. bena na we tu mejeparnga si takamina這邊. Acumuna tam du ku testekama. We are fuhama. We are fuhama. We need to see to connect here to connect here to only. This is the day. This is the day. Kwa na wimbo gani? Kwa tu kuja ni tu sa idea tu imbiem toto wa why why? A new song aki kuwam kubuata tu onapale YouTube Ikare bieni Wimbo ilikuwa gani? A thousand years Why why a thousand years?


Narcissist Ex-Boot reacts to Prince Harry and Meghan Markle. I am a narc-survivor and I am a Narcissist Ex-Boot. I have been studying Narcissist Personality Disorder for over three years. During that time I have worked with hundreds of clients including psychologists, psychotherapists and lawyers. I also have a YouTube channel with over 100,000 subscribers and over 24 million views. My expert opinion of Prince Harry and Meghan Markle's relationship is based on my lifetime of personal experience and three years of research. I believe that Meghan Markle is someone who has high narcissistic traits. When she targeted Prince Harry, she was not looking for a relationship. She did not intend to love or respect him. She targeted him based on her own self-interest and needs. She was looking for power and control. She wanted the ability to direct and influence people's behaviour and the course of events. Narcissists have to dominate people. They have to feel like they are in control. When a narcissist targets someone, they are looking for a person who is easy to control. A person who is easy to manipulate. And this is exactly what Meghan Markle did to Prince Harry. She had a plan of action designed to achieve a long-term result that is based on her own self-interest and needs. She targeted Prince Harry for a reason. He receives a lot of public attention. He is very wealthy. He has a high social and professional position. And Meghan saw this as a means to obtain power. She knew what type of person Prince Harry was. She knew that he was an empath. Narcissists deliberately target empathic people. They deliberately target people who show an ability to understand and share the feelings of another. While narcissists lack empathy, they lack the capacity to understand or feel what another person is experiencing. Which is how they can abandon people so easily. They will discard anyone who is no longer serving them. Anyone who is no longer doing what they want. Which is exactly what Meghan has done in her past. Her father said in an interview with TMZ Before Prince Harry and Meghan left the royal family My daughter dumped me one day before she got married. She dumped my family. She's dumped Doria Raglan's family. She's dumped every family. And now she's even dumping the British royal family. She divorced her ex-husband Trevor Engelsson a few years before she met Prince Harry. Some reports say that they split up due to irreconcilable differences or that he couldn't cope with her fame. But there have been claims that have said Trevor is extremely unhappy with his ex-wife. He has been quoted as saying he was devastated and that he felt like a piece of gum at the bottom of his shoe. It has been said that his eyes blazed with anger whenever Meghan's name was mentioned. Meghan targeted Prince Harry because he is an empath. Like his mother Princess Diana he cares a lot about the causes that he is involved in. And it can be seen in his interviews that he has a genuine concern for other people. Many of us have the desire to be recognised for our qualities and abilities. But this is something that narcissists see as a weakness. They see it as something that they can exploit. When Meghan first met Prince Harry she idealised him. She put him on a pedestal. She made him feel loved. Narcissists will be whatever they think you want them to be. They use a set of techniques known as cold reading without prior knowledge. They quickly obtain a great deal of information by analysing your body language, clothing, ethnicity, level of education and a matter of speech. They make use of their high probability guesses and then pick up on signals on whether their guesses are in the right direction or not. They then emphasise and reinforce their chance connections and quickly move on from any missed guesses. Narcissists will cold read what you want out of a relationship and then reflect it back to you. Meghan recognised that Prince Harry was looking for someone who was concerned with and seeking to promote human welfare. Someone who wanted to give assistance to people in need. Someone who was compassionate, generous and unselfish. Someone who was relaxed and not easily upset or worried. Someone who was low maintenance. Someone who was independent and not demanding a lot of attention. Someone who was down to travel to some of the most remote parts of the world. And this is the impression that she gave to him. Narcissists can manipulate people by compensating for their insecurities. By showing them they see them the way they want to be seen. Prince Harry was afraid of only being loved to be a prince or for being wealthy. So right from the beginning, Meghan acted as though she didn't know much about him. She acted as though she didn't care about his social or professional position. She acted as though she was only looking for someone who was kind. But as the relationship progresses it gets to a stage where the narcissist wants you to do everything that they expect you to do. They want you to prioritize their needs and desires. They expect you to pay them back. For all of the time that they invested into you. All of the time they spent making you feel loved. They want love from you and they also demand intense loyalty. Prince Harry was made to display his loyalty to Meghan by defending her against his family. Narcissists expect you to prioritize their needs and desires. They expect you to prioritize their emotions. And they will try to isolate you from your friends and family. This is why Prince Harry is always trying to defend Meghan. He does whatever she wants. A narcissist will make you do whatever they think will help them win. But they will never let you feel like they are winning. Because they always want more.  By playing the victim. Meghan wanted Prince Harry to think that everyone was against her. Everyone was harassing her. She wanted him to see her as though she gave up her entire life for him. And now her career isn't going anywhere. And this makes you feel guilty. If you care and love for them you don't want to see them hurt or upset. You want to fix all their problems. You want to protect them. And the narcissist loves it when you do this. They want you to spend all of your time trying to fix things for them. They want you to defend and support them. They want you to give them all the love that they could ever have wanted. But this stage doesn't last for long. It's only a matter of time until the narcissist gets bored. They don't want love and respect. They just want to feel like they're in control. They want to feel like they have power over you. And that is why they always end up devaluing you. It will feel like an emotional roller coaster. They will put you down. They will deliberately be unfriendly to you. They will give you the silent treatment. While making you think that nothing is wrong.  But it will make you feel miserable. The narcissist will switch back and forth between love bombing and devaluation. Their behaviour gradually gets worse and worse. They play on your insecurities. It makes you wonder what you did wrong. You don't expect this behaviour from someone you love. So it makes you work even harder. Because you want the good times to come back. It creates an addiction. At this point, some people will just leave. They're not going to want to tolerate this behaviour. But if you do try to leave. The narcissist will make you feel guilty. They will play the victim role.  They will act like they are going through a difficult time. They will act like they need your help and support. And if they're really cruel. They will even blame you for what they're going through. They will do whatever it takes to re-establish their sense of control. But even if you do stay. Eventually they will get bored. You will no longer be their primary focus. And they will be looking for someone else. Prince Harry is not at this stage with Meghan yet. But she has done this many times before. She did this to her ex-husband Trevor Engelsson. And also her ex-boyfriend Corey Vitiello. She was dating Corey when she first met Prince Harry. And their relationship ended. Just weeks before she started seeing him. It has been said that although Meghan and Corey were in a serious relationship. It hit the rocks. When Corey began to tire of her increasingly primordial behaviour. Which is typical behaviour of a narcissist. They are very temperamental. They are liable to unreasonable changes of mood. And they have an inflated view of their own talent and importance. They think they are more talented and important than they actually are. They are disapproving and difficult to please. They are vain and consider themselves too good to do certain tasks. Or live under conditions they consider to be inadequate. Their difficult behaviour can be very annoying. And this is what made Corey very upset. A woman's state that Meghan even took credit for Corey's past a dish. Her limelight stealing killed their connection. It can be distressing to be discarded by a narcissist. But it is actually the best thing that can happen. Other than walking out yourself. When the narcissist discards you.  They might try to hoover you.  But this is only because they don't want you to move on. They just want to keep you on their shelf. In case they need you in the future. They don't want to be with you. But they don't want you to stop thinking about them. Narcissists use your ability to empathise with people against you. But being an empath isn't a bad thing. It doesn't mean that people are always going to exploit you. It just means that narcissistic people will try to use these qualities against you. Which is why it is so important to educate yourself in this disorder. Check out my other videos about narcissists. And please share them with anyone who you believe may help. If you are interested in one-on-one coaching. You can email me at coachingatnaxviver.uk Thank you for watching and I will talk to you soon.


We looked largely at the biology, so there was not a lot of mathematics. We did a couple derivations. No, it's not true. We did do two bona fide derivations. But let me take you through just quickly what we did yesterday. So we're talking about cell division. This is the DNA, the chromosome. It gets replicated. Then the cell divides. We looked at some empirical relations. So basically what is sometimes called the fundamental results of bacterophysiology, these two back-to-back papers by Molas Group in 1958. So in steady state, and this is now balanced exponential growth, where you keep the cells in exponential growth for 10 generations before you take any measurements, they found that the RNA per cell increased basically exponentially with the doubling rate. At a higher rate than the mass per cell, which was, again, at a higher rate than the DNA per cell. They also did shift experiments, and you can rationalize the slope of these lines, at least for the mass per cell and the DNA per cell, by looking at the shift times and the kinetics. So if you go from a poor medium to a rich medium, the time it takes for each of these constituents, if you like, the mass, the DNA, and then the cell number to catch up to the new rate of division will give you the slopes of these lines on a log linear plot, which is surprising, but nonetheless we saw yesterday it was a self-consistency check, if you like. And it comes from the fact that these shifts are so abrupt, they're basically piecewise linear on a log scale. The RNA per cell, on the other hand, we rationalized in a different way, we rationalized it looking at the mechanics. What's really going on here? So that was something to do with the Neidhardt-Magasanic paper, where we saw that the rate of protein production by their assumption was proportional to the number of ribosomes, which then again was proportional to the RNA content in the cell, and that's what gave you this straight-line relationship at fast enough growth rates. With the interpretation that the slope of this line is inversely related to this translation rate, the number of amino acids that you make per second per ribosome. It's nice, it gives you an idea of mechanistic explanation for this increase in the RNA to protein ratio, and then possibly this increased slope in the RNA per cell. This connection between the slopes of these lines in these kinetic times is less clear. And so from about 1958 on, there was a search for some more detailed or mechanistic explanation for where these times come from and what was underlying the regulation of this switching to the new growth rates. So that's what we'll talk about today. It will probably take us till tomorrow as well, because it's an incredible experiment. So it takes some unpacking. But let me pause here. Are there any questions about what we did last lecture? No, I mean last day, so the last two lectures. Is that okay? And so I posted my notes on a link accessible from my home webpage, so if you have any trouble, try that out. Otherwise let me know and I can point you in the direction of the lecture notes and the course notes. Okay. So one of the big problems here with trying to infer mechanism, particularly at the level of single cells, is that all of these results are done on, say, 10 to the 9 cells or 10 to the 8 cells. It was a huge population. And so we're looking at population average results. And so the first question that we want to ask today, which will then lead us into resolving this issue later this lecture or maybe tomorrow's lecture, is when I say population average, precisely what probability density am I using to average? And what does the, for example, age distribution of these cells look like in a population? Okay. And so that's what we'll talk about today. And this is leading towards something called the Helmsteader Cooper experiments, but maybe I'll title this more dramatically as a search for synchrony. And by that I mean that in the 1950s, the technology wasn't yet developed to observe single cells in real time. The technology not yet developed to observe single cells. And so the genius of the biologists at this time was it, well, maybe we don't need to observe a single cell carefully. What if we could synchronize a population of 10 to the 8 cells? Then we wouldn't have to worry about measurement noise or anything like that. We would have this large population, but they would be synchronized. It would be acting as though they were a single cell. So the idea at the time was, can we synchronize the population, 10 to the 9, say, or 10 to the 8 cells? That would be effectively a large population of single cells, if you like, could be acting like an observable. I understand the reasoning here. So if this population is synchronized, everything in the population is doing the same thing at the same time, it's very much like just taking repeated measurements of a single cell. It's like an ergodic theorem, if you like. Yeah. Yeah, yeah, how do you know that they're synchronized without being looking? So one way you could do it is you could look and see if they all divide at the same time. Sure. Okay. Yeah, that's true. So you would have to come up with a criterion for what you mean by synchrony. And it will turn out that the criterion that we'll have is this division. So synchrony and age, they're the same age. Yeah, does that make sense? But then again, there would be an implicit assumption that the cell cycle within each cell is somehow the same. If you're at the same age, you're undergoing the same. And for a eukaryotic cell, that would be problematic for bacteria, it's not so bad. Okay, does everybody, is that any questions about this search? And so you can imagine maybe some tricks that you might try. One trick is that people try temperature shifts. So you would make them hot, cold, hot, cold, hot, cold, hot, cold. In the hopes that they would have, they would basically convulse into some sort of stasis. And then you would grow them normally and everybody would relax at the same time. Another trick was nutrient shift. And in fact, these experiments were designed to synchronize and they did not. Neither do temperature shifts. None of these things synchronize cells. And the reason that they don't synchronize cells is because the age is distributed through the population. Some cells are older and some cells are younger. And if you want to synchronize, that means you need to narrow that distribution to a delta function. And playing with temperature, playing with shifts, all it does is move that distribution around. So you don't have to narrow it in any reasonable sense. So what I want to talk about first is what is this distribution that I keep indicating with my hands. And then second of all, how can we resolve this? Or how did they resolve this? And I'll maybe give you a little foreshadowing, which is that it turns out to be more or less impossible to synchronize bacteria. But what you can do is sample, in a very clever way, sample strips from the population distribution in time, which serves the same purpose. I mean, it wasn't really designed to make sense at this point, but that's where we're headed. All right. So then first, what is the distribution ages in the population? What I mean by that is how close are some cells to dividing, or how close are cells to dividing? What's the distribution of that age, if you like? So by age, I mean, age here, I'm going to denote by A, and it's anything between zero and tau, where this is the doubling time or division time. And so you can have newborn cells, which have age zero by definition. And then you can have very old cells, according to their life cycle, which would be tau minus epsilon. And so we're going to work this out, what this age distribution is. But just intuitively, yeah, Matteo. It wouldn't be also the age of the division time, but in this case, I'm not. And so it could be that A is actually going to go from zero to infinity, but we're going to find that it's compactly supported if I make the assumption that tau is a delta function. But we don't need that. So in the derivation, I'm going to leave the distribution as the doubling times or division times as a distribution. And then when we get to the end and we want to normalize the distribution, that's when we're going to put in some additional assumptions just to make it a little bit easier. But for now, I mean this conceptually, you're right. You're free to go further, and some will. Is that okay with today? Yeah, sorry. Yeah, yeah. Yeah. Yeah. Oh, it ceases to be the mother at that point. No, no, no. I mean, it's not, it's not semantic. It means, I mean that it really does reset. So the two that come off at the end go back to the beginning.  You're right. And Matteo's point is that it's not a hard wall. I put it up here just to, so you have a sense of what I mean by age, but think of this tau as a sort of a fuzzy ending to their doubling cycle. Or if you like, you can think of it as a delta distributed. Everybody divides exactly 40 minutes after birth. That's conceptually fine as well. But is that okay? So this modularity is important, and we'll come back to it in one second. But you had a question? No. That was it. Okay, now my question is, given this modularity that he suggested, what can you tell me qualitatively about this population distribution? Anything? Uniform. Uniform, okay. Can it be uniform? Okay, Gaussian and uniform are perfectly legitimate, knee-jerk suggestions. Which is of course, as a physicist, that's what you would, I mean, that's what I would say. If it's not uniform, it's either Poisson or Gaussian. And that's totally legitimate. But there's something that we know about this process that's, if you like, unique to this system, which is exactly what you were saying, right, that mothers become two daughters. What does that imply about the population distribution? Pardon me? It's sort of power law, but then, maybe I'm not framing it well. Do you expect more young cells or more old cells? More young cells. Young cells. And how many more? Twice as many. There's always twice as many young cells in your population as there are old cells. Because all the time, the old cells are having, they're dividing into two. Which is very weird. I mean, now you can rationalize it backwards, but it's odd that no matter what distribution you have for these doubling times or whatever it is, you are going to have twice as many young cells as you have old cells. And what we'll do is analytically derive what this distribution needs to be, and you'll see that that is indeed true. But just qualitatively, I hope it makes sense, that because these cells grow, grow, grow, then divide and sort of recycle again, you're always dumping in from the end of the distribution, you're dumping back in again to the front twice as many. So it's like a periodic boundary condition with amplification, if you like. I don't know if that's helpful. Yeah? All right. And so we know qualitatively, twice as many newborn cells, cells about to divide. Divided. But what precisely is the distribution? And so let me introduce some notation and then let's manipulate this distribution until we can solve for it. So I'll give you a sort of, what would you call it, a synopsis of what we're about to do. I'm going to define these probability distributions, both for the division time and for the age distribution. And then we're going to use properties of statistical distributions, namely that you can look at cumulative probabilities to end up with a difference equation for that distribution, which is going to be horrible. But then we can use Taylor series to turn that into a differential equation which we can solve, lickety-split. And once we have that, of course, end normalization becomes an issue. And so we'll normalize after making an assumption about this distribution for these doubling times. It's not necessary, but for us it's fine. For what we're going to use this distribution for, it'll be sufficient. So let me first define what I mean by these distributions or what notation I'm going to use and then let's talk about it. So the cell age distribution or the age distribution is denoted by, well, I will denote it by phi A. And what I mean is that it's a continuous distribution which represents a probability that A bacterium aged between A plus DA, however you want to do this, A minus DA over 2, however, in some interval of width DA. To divide. Because the newborn cells will take pretty much the same time as their mothers for dividing. Yeah, more that mothers are dumping, every time they divide, they dump in two newborns. So the instant that they divide... Why are you calling them able to divide? They are as able to divide as the newborns. Cells about to divide. Oh, I mean at the threshold of division, their age is tau. Sorry, is that not clear? So cells about to divide, i.e. their age is about tau. So A approximately equal to tau is what I mean. I mean they're at the end of their career as a single cell. Is that better? No? Is it the about or is it what do I mean? Okay, what do we talk about? Okay, is this okay, this distribution? What do I mean by this? Okay, let me talk then about the distribution for the doubling times.  Let me pause it. So these are going to be the two, the two sort of things that we're going to be playing with. This one we're going to be, we're going to assume it's a given. This is our input, if you like, and we want to find this output. So we need to find an equation that's going to transform our given distribution of doubling times to some probability of ages, if that makes sense, I hope. Is that sensible? Let's take a look. So I'm going to move this down so that I can use the board, but hopefully a between tau and tau plus d tau. All right, so the first step is going to be to look at the cumulative distribution of this doubling time. So I'm going to integrate it from some time up to infinity. I'll do that in one moment. But one thing that I want to call your attention to is that I'm going to be thinking of this as a steady-state distribution. And so there'll be no time dependence in this distribution for now. Well, forever in this course, but... All right, so this guy's steady-state. Now let's look at the cumulative distribution. So we'll introduce cumulative density. This is going to be called F greater than, which is the fraction of cells with doubling time. Okay, so you can think of it as the complement of the... Sure, I could call it A cumulative density then, rather than D. And so by definition, we'll have this. Well, let me put it... Let me put primes here, sorry. There we go. And so this is really the extent of the probability theory that we need. And now what we're going to do is manipulate this and try... Oh, sorry. And try to express a certain fraction in a second in two different ways. And that'll give us our difference equation. But let me pause. Is the notation comfortable for everybody? Anyone have any questions about notation? Yeah. This guy? Yeah, to the quantity of the age and the probability of the whole duration, like for example, a person can live 100 years, but then you're calculating how many... the probability of having age between, for example, 5 and 10. Exactly, exactly. But how can you calculate the mean division? Yeah, so this is an input. We either need to measure this or just guess what it might be. And here a Gaussian distribution would be maybe a sensible guess. Or something like this. Yeah, you would have to either have a guess or some empirical reason for your choice. You might even try a uniform between two bounds. But the idea here is that given this distribution, we want to chug it through the biology to get this distribution. Yeah, possibly. I mean within reason. But here what we're thinking of is steady state at a single growth rate. And that'll be important. If you want to do shifts and things like that, then you'll need to modify this derivation. But you should have enough tools to do that if you want it to. It's okay? Alright, let's take a look. Alright, so suppose that we have a bacterium that reaches age A. So then what is the probability that it will reach age A plus T without dividing? And this is kind of one of those classic assignment question in probability and statistics. But let's work through it. So is that comfortable? So we've got them, we know that we're at age A, whatever that age might be. We have some finite interval, A plus T, and I haven't said what, you know, T is just some finite interval number. And we want to know what's the probability of getting that far without dividing? Okay, so here my delta T is just T. So you can think of this as delta T. Is that okay? No? Okay, alright. So let's look at it. This is age A, this is age T, this is age infinity. Alright, and so this, we go like this, F greater than A is the fraction with doubling time greater than A. By definition, that makes sense. And in this one, this will be F greater than A plus T, which is the fraction with doubling time greater than T, or sorry, greater than A plus T, if that makes sense. Is that alright? That's by definition. Okay, now we want the fraction right like this. So given the bacterium reaches age A, probability, no division in this interval A to A plus T is going to be equal to one. And you can either tell me directly or you can, we can argue pictorially and you can tell me what element of this picture I'm talking about. Can you say one more time? Yeah, I agree. So what is this fraction? This fraction is probability that no division occurs between 0 and A plus T. Is that true? So the point here is that we've got only this rectangle to worry about. We've said because it's a conditional probability we're at all this stuff with probability one we've reached age A. Okay, so this dark rectangle is going to be the fraction with doubling time between A and A plus T. Exactly. Can I pause for one second? I'll just pause. Take a look at that and tell me if you believe it. Now given that rectangle what's the fraction of that rectangle? Of course it's problematic because one of the sides of the rectangle is infinitely far away but you can just bend yourself there. The doubling time and the division time same thing, sorry. So a doubling time is the division time. They're synonymous. Same. So they divide the numbers double. So I want the light part of this I want to know what fraction of that rectangle is not hatched. Does not have lines on it. Yeah, that's true. That's true that this might, this is optimistic that it's probably starts to be one after that but it still stands if T is sort of small enough then you would think that there is an appreciable fraction that is here and appreciable fraction that's here. It doesn't really matter for us if it's appreciable or not. Just abstractly what would be the fraction of this rectangle. It's not this but that was a good guess. That would be if A is 0. So I'm going to write it. There are a couple of suggestions up here but it's the ratio of this to this because what we're interested in is this piece. We want to know the relative area of that piece relative to the whole rectangle. Let me write it up and you tell me if you believe it. This is going to be f greater than A plus T divided by f greater than A. And that's going to be the area of the part of the rectangle that's kind of next through it. So two questions. One, does that match your intuition for what these functions are representing? And two, does everybody see what I'm trying to calculate? Anybody Nazi? Anybody want to back up a bit? Is that okay? I guess maybe not okay. Okay is not the word. Does that seem reasonable? Yeah? Alright. Okay. So here what I'm asking is given that you start here, what's the probability that you make it here rather than dividing here? Okay and the way that we do that is we'll ask what the probability is for this whole rectangle and then look at the probability that you missed the hatched part of it. And undoubtedly you can manipulate that in different ways. Right? But what I want to do is look at it as this fraction because I want to express it then in terms of this age distribution at the moment. Alright so if we have that, let's start fiddling with it. So now suppose we start N bacteria with age zero. So we have a perfectly synchronized initial population. Now I want to ask how we write that fraction in terms of this exponentially growing population. So the number of bacteria at age a a plus d a will be so if I start with N bacteria at age zero and then I have this distribution what's the I shouldn't have put them at age zero. Sorry. Start with N bacteria. Suppose we have N bacteria. What's the number of bacteria that have an age between a and a a plus d a? Given that we have a probability distribution for the age. Yes. So we'll get N multiplied by phi a d a. Does that make sense? So this instant right now now suppose we wait a time t what's going to happen? So now let me write one more thing and let's talk about it. Number undivided a plus t is going to be this. So this will be number undivided age a plus t will now be what? So suppose I have that many bacteria and if that fraction I can multiply the two and so I'll write this up and let's talk about it. By a d a times this fraction I promise you we're getting somewhere for right at the threshold of getting somewhere. So far so good. This is the number that are at this age so that's the number that are here and then we have this fraction that makes it for a finite step delta t or t in this case. So far so good. So does this match then with your intuition for what these functions mean? It's okay? Alright. Here's where the biology comes in. So over this interval a plus t the population increases. So suppose I'm imagining he's exponentially growing cells in a steady state what's going to happen over in finite interval or non-zero interval t will the population increase too? Did I give you enough to go on? What's that? So we have n cells right now these cells are in balanced exponential growth. We wait to this time so at time a so t is equal to 0 we have n cells at time t is equal to t we have how many cells? After a period t what happens? What's the population? So t is a finite amount of time what's lurking behind here is we're in balanced exponential growth so what can you tell me about this population? Think of n as being so large that our population is continuous I feel like I'm not giving enough information I'm going to write it up and you tell me if this is true wait maybe that's what you were saying were you using a base 2? So you were saying 2 to the doubling rate times t is that what you're saying? Because this is also the same thing as n 2t divided by some doubling rate t times mu some average doubling rate What's that? Yeah we need to we're eventually going to get f back again Oh I see Okay I think we should pause and kind of step through this okay so your cells are growing exponentially balanced exponential growth we have this idea that we have a distribution for their ages we don't know what that is we have a distribution for their doubling times we also don't really know what that is but empirically we do know that the population itself is growing exponentially and so then the question is given that I know this is true so this is going to be my empirical input or constraint that I need to satisfy that I have some unknown function for the doubling times and for the cell age what can I do with it how can I find this from this and this right but this is an empirical constraint that we have to deal with the cells are doubling exponentially obviously irrespective of I mean if we were free to choose any distribution of doubling times imaginable probably we could no we couldn't we can't break that we don't know what the distribution of doubling times is precisely but we do know that the cells are growing exponentially is that does everybody is that okay do you agree that this end over this interval will have to increase exponentially okay so then if we want to look at let me go one more step and then let's talk about it so then the fraction undivided cells is a filing it will be then fraction undivided a plus t will be this big mess and then let's talk about it greater than a plus t f greater than a t a divided by n e lambda t so this is the number that are undivided at a plus t but this is the total population size at time a plus t and so the fraction is dividing both of these and so if I carry one more step I will get let me do it here I will get by a f greater than a plus t f greater than a by a and disappears by e minus t okay but then I want to express this as a fraction I'm assuming all of these cells are independent so this is also a probability what probability is it which is the same as maybe it's best if I write it up here i.e. the probability a cell has age a plus t to a plus t plus d so let's pause the threshold now of actually being able to derive an equation for that phi irrespective of what the distribution of doubling times is okay so let's go back to this guy is that one let's go way back okay and in this empirical constraint that our cells are increasing exponentially and we have a fraction of undivided is going to be that number divided by this total population and then we tidy it up a bit and then we just cancel this exponential I'm putting in the numerator but then I look at that this is the fraction that are undivided at a plus t so then that tells me that this is a probability that a cell has an age a plus t an a plus t plus d a is that okay and now my question to you is is there another way to write that you exactly right so in terms of phi what would it be exactly phi a plus t d a and so this where we've advanced the probability distribution ahead by a finite increment is equal to this and that gives us our difference equation so let me leave that up and then let's let me rewrite it over here phi an a plus t and I'll pause here and then we can talk about it equals phi greater than a plus t over greater than a e minus t and so the problem then becomes you give me a distribution of doubling times and you obviously also need to tell me the growth rate of the population those are my inputs and then it's incumbent upon me to solve this difference equation for phi it's subject of course to normalization things like that and it's horrible you don't want to solve this thing but anyway let's talk about and make sure that it's okay and what we'll do is take a Taylor series for small t and solve the differential equation and then what I ask you to do is an exercise at the end of those lecture notes is prove that the distribution you get from the Taylor series also satisfies the difference equation but for now let's just take the Taylor series but before I do that is this equivalence comfortable anybody have any questions about this equivalence and so I wouldn't expect you to reproduce this argument it's far too many steps for a person to keep in their head so don't worry about memorizing this it's more important to me that you can you can see that it's baby step baby step baby step baby step gives you what crazy solution in the end alright and I'm actually even more interested that you see the distribution later even qualitatively but I want to take you through the calculation once so that if you felt like it in future you could go through it without any trouble with a minimal amount of labor alright so that said is this equivalence comfortable and so then we have this difference equation how do we solve it so how do we solve this alright so we will use a perturbation expansion so we will use a Taylor series for t very small ok so maybe we'll do that we'll take a break for maybe 5-10 minutes or something and we'll come back and solve this guy but before we go any questions before you go alright they might develop so yeah I'll see you in a bit to hand this out again yeah for sure give you before which is this Bayes theorem ok and that's that's his derivation and so just to remind you so I'm going back to the rectangle that I had which I think was not so great maybe so this is f greater than a plus t and then I had this guy which is f greater than a alright and what we were looking for was again the probability so given the age age what is the probability no division between a and a plus t i.e. it's a survival probability that you reach the age a plus t ok and so just to remind you this is Bayes theorem we've got this conditional probability is expressible as a joint divided by the initial probability if you like and so in terms of what we're talking about we're looking for the conditional probability that given that the doubling time is greater than my present age what is the probability that the doubling time is also greater than my age plus t alright so this conditional probability is precisely what we're after is that clear clearer I hope probably than this rectangle but then we can express that as this joint probability that the doubling time is bigger than a plus t and the doubling time is bigger than a divided by the probability that the doubling time is bigger than a so far so good we pause alright now it's lovely inside is that this is a redundant restriction that if the doubling time is greater than a plus t t is non-zero and positive then this is automatically true it's redundant the first condition implies the second and so then you end up with this probability that the doubling time is greater than my age plus t divided by the probability that the doubling time is greater than my age but then that's just expressible in terms of a cumulative function f greater than a plus t divided by f greater than and so that rectangle that I showed earlier was a misguided attempt at circumventing phase is that okay? I hope that's better for those for whom this the rectangle is not good hopefully this brings this all together does it? good so that's the new way that I will teach this, thanks alright so let's go to the Taylor series I'll leave that up if you want and we'll come back to it okay so if we take this use a Taylor series with t going to zero then we can re-express these finite increments as infinitesimal changes so we'll Taylor expand this we'll also Taylor expand this okay so we have that f greater than a plus t and we have phi a plus t and we have e negative lambda t only here am I going to keep the order symbol so I'm only going to take it up to first order and then I'm going to throw out all the order t squared stuff okay so what I end up with is f greater than a plus t f prime greater than a plus t phi prime of a and then here I get 1 minus lambda t and all these are plus some order t squared okay and I'm going to truncate here and ignore the rest is that okay everybody's okay with this Taylor series so the idea is that I want to get rid of this finite increment and so now if I plug that into here what do I get the first step is a mess with a little bit of algebraic manipulation we can pull it together maybe I'll pass this around I always forget to pass this around alright so then if we put this into our difference equation it becomes this we'll end up with phi prime of a over phi of a is equal to f greater than a prime f greater than this is nice and we get this ratio of derivatives over their functions and so this immediately suggests to us that we start using natural logarithms the next step is less obvious but you'll be able to see in retrospect that it's okay so let me write that up and then let's talk about it this is da times the natural logarithm of phi of a is equal to d by da the natural logarithm of and normally we would just be looking at the natural logarithm of this guy but that lambda is going to give us a little bit of trouble except that we can group everybody together e negative lambda a so if I've done everything correctly I think that that will give you the same expression and so now what we have is a separable differential equation before it didn't look like it it looked horrible I guess you could see that it was a little bit separable but anyway here's a better form for it and so we can integrate let me pause though from here to here via this is I hope okay any questions though it's okay so from here to here okay at least in retrospect I mean I don't think any same person would rewrite this like this without knowing what the answer was alright so if we integrate we'll get phi of a is equal to some normalization constant which we don't know yet e negative lambda a f greater than a which we can now rewrite in terms of our our distribution for doubling times so now we have phi zero which is this normalization constant and I'll come to that in a second times this integral from a to infinity of f of tau prime and that in in principle is our distribution for ages which is contingent or relies upon this assumption that my population is growing exponentially and it's in some balanced state of growth alright and so we haven't said anything about f yet this distribution of doubling times nor have I said anything about the normalization condition but we'll come to that are there any questions about the solution of this differential equation first off does this seem reasonable alright even without looking at a particular value of this distribution function or this normalization qualitatively can you say anything even without an explicit what can you say about two term and this term as a gets larger so phi at zero is newborn cells and now as a function of a what can you say about the remaining two terms you got it they're monotonically decreasing the exponential I think is okay this guy's monotonically decreasing with a this guy is two though it doesn't matter what this probability distribution is this one minus accumulative is always going to be monotonically decreasing and so we know that this guy is as big as the distribution gets there are always more newborn cells it doesn't matter what your distribution is um phi zero is always the max e negative lambda a and this integral monotone decreasing and so now this comes from a derivation by Powell from 1957 to derive the normalization condition for arbitrary f but we don't need to do that I mean if you're interested you can look at how he does it but for us what I'm going to look at is a delta distributed distribution or a delta distributed um doubling times so it's possible to solve for the normalization arbitrarily but it's a lot of work well not a lot but it's work alright so for us it is, it will be sufficient to consider delta distributed doubling times or division times so this f tau prime is going to just be a delta distribution a direct delta distribution around some macroscopic or fixed doubling time so this will then give us that phi a phi a is going to be phi at 0 e negative lambda a or 0 so this is for a 0 and tau and this is otherwise if I did that right sorry which part this part ok so suppose now we put a delta function so the delta function is 0 except for one point and then if we integrate across that point then we get 1 and so if a is above tau this delta function will be over here in the interval we'll miss it, we won't integrate across it does that make sense but then if the a is going to be less than tau then we'll have a delta function that will integrate over and we'll get 1 and so this thing is either going to be 1 depending if a is greater or less than tau ok let me write that up and then let's talk about it for one more second i.e. we have that this integral delta t prime minus tau dt prime is equal to 1 if a is less than tau and 0 if a is greater than tau then your definition of how to integrate the delta function you could put an equal to sign on the top one or the bottom but let's I'll just leave it, unless it drives you crazy in which case we can decide what we want to do with it so everybody understand what I'm saying so it's not well defined when I integrate with this tau right at one of the boundaries is what I'm saying so I'm going to ignore the boundary and I'm going to pass now is that distribution is this function now sensible given this definition for the delta function it's okay any concerns good so now we'll look at the normalization and then we'll be we'll be able to plot this guy and then we'll be done so after normalization i.e. enforcing this condition the continuity of phi a d a is equal to 1 we end up with the following solution for phi 0 we get phi of a is equal to and you can do this if you like or you can take my word for it e negative lambda a right so long as a is less than tau but I'm going to make one more change in a second but then we know that I mean in this case where the tau is a macroscopic doubling time that that means we're just rewriting the natural base e in a base 2 if you like and so this lambda which is my exponential growth rate is related to tau which is my base 2 doubling rate by the natural logarithm of 2 so this thing let me write one more thing which is that lambda is equal to long 2 over tau if we had a general distribution for the doubling times that wouldn't be true and so that's another hassle about dealing with generalized distributions for the doubling time but for delta distributed that's by definition true okay this is the time it takes me to increment by a factor of 2 this is the time it takes me to increment by a factor of 2.7 and so then I end up with let me write one more line and let's talk about it 2 long 2 divided by tau 2 minus a over tau for a up to 1 and so let me pause first of all is that okay? does it mix with the definitions we've been using so far is basically my point anybody feel okay and so normally or often or often we we use a relative h say a hat which I'm going to divide by tau in which case this distribution becomes the following and I do this just because I want to be able to write it in a very compact way so then we get phi of a hat is going to be equal to 2 long 2 of 2 raised to the negative a hat for a hat going between 0 and 1 now my question is okay let me pause there's been a lot of algebra hidden underneath the sink here but this is the this in the end is what I wanted to get at today I wanted to get at this because for two reasons well for one main reason is because when we look at the experiments that were done on trying to synchronize cells this distribution is going to show up and it's important to see where it came from I think but before that what does this distribution look like this is phi this guy so this is only for this f of tau prime equal to t minus t prime that's part of the problem with the general distribution is not only do you need to normalize you also need to relate the empirical doubling time to this distribution to some moment of that distribution does that make sense and so that derivation I'll post that paper and you can look through it so it's not part of the papers that I have on the website right now but I'll make it part of that web those papers do you know what I mean if you're interested in the general derivation I'll put it up on the website for this part it's okay so if you are interested in the more general argument I'll make that available to you let me pause though any questions it's okay alright what's this distribution look like that there's a question this guy minus oh wait no because it's in the basement I know you're right negative land yeah thanks yeah very nice okay what does this function look like yeah perfect it just looks like this and so this thing is two long two and this thing is one and so the relative abundance of babies is twice as much as their mothers if you like or not that's not quite right they're twice as much as those just about to have babies or just about to divide alright let me pause any questions about any of these okay alright so this distribution is where we're gonna start I don't know when this one ends does this one end what's the time that these things end at 11 10 oh okay okay alright so maybe I'll say ah you know this is a good place to stop so next next time so that will be tomorrow at 11 we'll we'll start with this distribution and so the genius of a guy named Helmstetter is that he's gonna come up with an apparatus that samples as a function of time tiny strips from this distribution and so essentially he has a time series of synchronized cells and it took him 10 years to come up with this idea and um maybe I'll give you alright I'll give you just one sort of um what do you call it foreshadowing that he imagined himself lying in bed and a bunch of chickens on his ceiling dropping eggs on his head and that was the sort of the epiphany for him so with that in mind imagine how you would sample this distribution and we'll talk about that tomorrow but let me pause again any questions about this so the details are in the lecture notes and in the course notes and as I say I'll make the more general derivation available through the website it's okay? alright ok see you guys tomorrow