He said it was resonance.
Not only did this describe Sir Paul's work, but also the impact he would leave behind, Mr Allport said.
"I believe everything Paul has been will go on resonating.''
Sir Paul's very public battle with cancer since 2008 meant he had time to prepare his funeral and Mr Allport said that although Sir Paul was not particularly religious, he chose to have his funeral at Wesley Church because churches were not just a place of worship but a place of higher learning.
His uncle also used to be a minister at the church.
As well as organising his own funeral, Sir Paul left instructions for everyone to sing the hymns "lustily''.
"Paul will be delighted with your efforts,'' Mr Allport assured the mourners after singing To Be a Pilgrim.
A theme throughout the service was his love for his children Catherine and Chris Callaghan, his two grandsons James and Thomas, and his second wife Miang Lim.
Catherine Callaghan described her father as full of "boundless energy, enthusiasm, imagination, humour, knowledge, wisdom, kindness, [and] generosity''.
"It made him an extraordinary dad and grandpa.''
She spoke of growing up in a family thinking it was perfectly normal to sit around the dinner table discussing everything from the injustice of Parihaka to the viscosity of ketchup.
"He didn't just talk, he was a man of action, a hands-on dad,'' Ms Callaghan said.
"When he wasn't being crazy, he could be incredibly wise.''
Sir Paul's accolades and achievements make for a long list, including the Rutherford Prize, the Sir Peter Blake medal for leadership, Principal Companion of the New Zealand Order of Merit, the international Gadiunther Laukien prize, and 2011 New Zealander of the Year.
He launched the MacDiarmid Institute in Wellington and set up the company Magritek, to make and sell portable nuclear magnetic resonance measuring devices.
Andrew Coy, a former PHD student and now chief executive of Magritek, spoke of Sir Paul's tireless work ethic.
"He believed in us, he believed absolutely you would achieve those goals,'' Mr Coy said.
"He would support you every step of the way...he passionately wanted us to be successful.''
Sir Paul's brother Jim spoke of their childhood in Wanganui and his inquiring mind even at a young age at school.
The two brothers once set out to find their uncle's old farm in the middle of nowhere.
Once the farm had been found Mr Callaghan thought that was the end of the quest, but Sir Paul went on to research the area and produce a pamphlet on it.
"Half-hearted was never a word in Paul's vocabulary.''
Sir Paul's body would be cremated in Wellington and his ashes taken to Wanganui to a "special resting place'', his family has said.
His funeral was broadcast live at Victoria University, as well as online, to prevent congestion at the church.
Dignitaries at the funeral included Governor-General Sir Jerry Mateparae, Deputy Prime Minister Bill English and Wellington Mayor Celia Wade-Brown.
