Belief is a powerful thing. It can spark wars, fuel revolutions and inspire religions.
It can be seen in masses of people marching across rivers and turned towards the Sun in prayer. It can be heard in a choir of voices singing from the same hymn sheet, and in a single one roaring through a megaphone. It can be touched in the smooth stones of cathedrals and the rough cobbles of castles built by many hands over time.
Over the past few weeks, as the Socceroos have prepared themselves for their opening World Cup game against France, that word – belief – had become the foundation upon which the team's idea of itself was being constructed.
It wasn't always in that arrangement of letters, but it was there. Whether it was the "Aussie DNA" or reference to the "spirit" or "identity" of the Socceroos, this intangible thing was there, laid down like mortar beneath the lines of every player and staff member who was asked about how Australia could surpass the potentially unsurpassable: the reigning World Cup champions.
"We've built the belief and the energy and the focus," coach Graham Arnold said.
"Over the last week, since we've been in camp, we've been working hard on building that belief."
Belief is a useful tool for an underdog side to lean into the intangibles when the tangibles are so heavily stacked against you.
This was a France squad that, despite a string of injuries to key players, was still fourth in the world and able to field a starting XI containing regulars at the world's biggest clubs.
When Ballon D'Or winner and centre-forward Karim Benzema withdrew from the team late, they simply started the country's now equal-highest goal-scorer, Olivier Giroud, instead.
When they lost their starting left back, Lucas Hernandez, early in the first half, they simply replaced him with another Hernandez brother – Theo this time – who assisted France's equaliser and was world-class throughout.
When the creative force of Paul Pogba was unavailable, they simply moved Antoine Griezmann slightly in-field and started Ousmane Dembélé out wide; the Barcelona winger mirroring the untouchable Kylian Mbappé on the other side of the field.
But this World Cup has already witnessed how belief can manifest into something tangible, as when Saudi Arabia – ranked 52nd in the world – defeated Argentina earlier in the day: a team that sat 50 places above them, which contained perhaps the game's greatest ever player, and who hadn't lost a game in almost three years. It was enough to make you believe in castles in the sky.
And in the opening 20 minutes of Wednesday morning's game, the Socceroos had all of us crossing the drawbridge.
They may not have had much of the ball, but they didn't need it to do what they wanted. Settling into two tight defensive lines, and with the speed of Mat Leckie and Craig Goodwin on either flank, Australia's plan was to lure France out from the safety of their own doorway before sticking the knife in sideways.
It took just eight minutes to do so. A long, raking pass by the towering Harry Souttar found Leckie on the right wing, whose delicate in-field touch sent his opponent sprawling in the grass.
Leckie's cross appeared too heavy for Australia's galloping forward, Mitch Duke, who threw his head backwards in frustration after thinking he'd been beaten by its pace, but the ball was never meant for him; it was meant, instead, for Goodwin, whisking in at the back post.
Until that point, Al Janoub in Doha's south had just been a stadium: a structure of sweeping steel and glass with a football pitch in the middle. But when the ball thwacked off Goodwin's in-step and past Hugo Lloris into the roof of the net, it became something else: it became Sydney in 2005, Kaiserslauten in 2006, Nelspruit in 2010. A place where miracles really could happen.
It felt fitting that Goodwin's celebration resembled that of a man in prayer, falling to his knees while pointing two hands to the sky.
There it was again – belief – filling up that once-empty space like a balloon. Was this what Arnold was talking about? This feeling? There goes Mitch Duke's bullet strike sizzling just past one post. Surely it's not possible? Jackson Irvine's header bounces in slow-motion off the other. It happened against Uruguay, against Japan, against Serbia, could it happen against France? Could it?
But this is the problem with belief: it only exists for as long as reality keeps itself at a distance. And in the 27th minute, the cold facts of Australia's circumstances arrived.
It came in the tenacity of Adrien Rabiot, who equalised with a glancing header. It came in the awareness and strength of Giroud, who scored a brace to equal Thierry Henry's international record. It came in the creativity of Griezmann, the breakwall strength of Dayot Upamecano and Ibrahima Konaté, the dazzling guile of Dembélé, the commanding presence of Lloris.
But most of all, it came in Mbappé: in the angles and shapes his body makes when it hits warp-speed, the brightest star in a galaxy of stars, who danced down the left wing all night and gave the shell-shocked Nathaniel Atkinson the harshest possible introduction to international football.
When you look at the numbers, that it was only 4-1 at the end of the 90 minutes was perhaps the most unbelievable thing about it all: France tallied 23 shots to Australia's four, 7-1 on target, eight times as many corners and almost twice as many passes to get them. And this, we told ourselves, was a France side that starts these tournaments slow.
In the end, then, it wasn't about belief. It was about what football is always about: players and tactics and fitness and skill. It was about the reality of all this; the world outside the castle walls.
As Arnold conceded afterwards: "At the end of the day, the quality of the French team [was the difference]. They are the previous world champions for a reason.
"Physically, they were just so much bigger and faster and stronger than us today. But overall, the boys did everything they could and that's all I can ask."
Reality is that which, when you stop believing it, doesn't go away.
On Wednesday, we watched the Socceroos' castle of belief crumble before our eyes.
With their second group game against Tunisia less than a week away, time is running out for them to re-lay their stones with something stronger and more real than words of air.
