Ukrainians are showing exceptional courage as they fight off Putin's forces. Russian troops took control of no large population centers by the fourth day of the assault. The Russian-speaking second city of Kharkiv was resisting. Western democracies have found the will to impose sanctions of unforeseen severity, targeting Moscow's central bank reserves and barring some lenders from the Swift messaging system. The plans for a walkover by the Russian president have been confused.

Putin's war looks like a mistake. That could make him more dangerous. Putin put his nuclear forces on high alert on Sunday as his Ukrainian counterpart agreed to talks on the border.

The rebuilding of its military has reflected in the intensity of the resistance. This is no longer the raggle-taggle force that was caught off guard by Russia's aggression. The western allies helped to train it. Anti-tank and anti-aircraft missiles supplied by some foreign partners have aided in slowing Russia's advance and ability to take control of the skies.

The spirit of Ukraine's people is shown by the defiance. The sense of national identity that has solidified from the Ukrainian-speaking, Europe-leaning west deep into the Russian-speaking east is confirmed by this. Ukrainian warships are displaying great bravery, from civilians mass-produced Molotov cocktails to border guards responding with a Russian expletive to a Moscow demanding their surrender. They are evincing a common humanity through efforts such as a hotline for families of killed and captured Russian soldiers. The war leader is a comic-actor president who refused to flee the capital.

After being shocked by Putin's aggression and shamed by their failure to do more to avert it, international democracies have responded with financial and economic measures. Germany pledged a huge boost to military spending after dropping its longstanding refusal to export arms to conflict zones. Swift sanctions and the central bank are steps towards shutting Russia out of the financial system. Russians were waiting at banks and ATMs to withdraw cash.

Russia's invasion of Ukraine: what next?

The military of Ukraine is still facing a lot of odds. Every day it holds back Putin's forces. The effects of western financial sanctions are amplified by the Ukrainian resistance. New risks are involved in this. The collapse of the rouble and prices could cause a backlash among Russians who never wanted this war against the west. Communications aimed at cutting through state propaganda are vital.

Slow progress in Ukraine will prompt Putin to order his army to use its more terrifyingly destructive weapons against civilians too. Russia's president could be tempted to go beyond Ukraine. Placing his nuclear forces on alert, aiming to intimidate the west, is a dangerous escalation by a leader who has made Russia's nuclear doctrine more threatening since the Soviet era. The risk of Putin trying to go further was raised by a swift subjugation of his neighbour. There is a perilous moment in the world. Ukrainians are teaching it a lesson.