This amusing story tells little about the Subtle Doctor (who, alas, never informed the posterity about his hats) but it correctly reflects the folk wisdom that pointed hats relate to (forbidden) learning and dark perversions of medieval mind. Fairy tale wizards and witches always wear such hats. So do fairy tale princesses. They were ignorant people believing in the transformative power of cone shaped hats, as opposed to 21st century folk believing in the transformative power of chat shows streaming through the apex of their TV antennas.
As far as I can tell, the first people who wore pointed hats in medieval Europe were the Ashkenazi, and such hats quickly became associated with Jewishness, to an astonishing degree. J. Paul Getty museum has a fantastic piece called the Road to Emmaus
that shows Jesus and his companions in Judenhuts.
...unlike the yellow badge, the Jewish hat is often seen in illustrated Hebrew manuscripts, and was later included by German Jews in their seals and coats of arms, suggesting that at least initially it was regarded by European Jews as "an element of traditional garb, rather than an imposed discrimination". The hat is also worn in Christian pictures by figures such as St Joseph and sometimes Jesus. However, once made obligatory, the hat, hitherto deliberately different from hats worn by Christians, was viewed by Jews in a negative light. http://en.wikipedia.org/wiki/Jewish
Until the funnels became compulsory, the Ashkenazim loved these silly looking hats as dearly as the Hasidim love their shtreimels. Then these hats fell out of favor, and the Christians became worried, as they got used to the Judenhut to tell the Jews apart from themselves. Around 1250 AD, various states and municipalities legislated compulsory wearing of such hats by the Jews. As the latter were also habitually blamed for magic and occult, a connection was firmed in European mind between the suspicious learning and such hats.
Around the same time Sufi fraternities started using conical hats in whirling dances that impersonate the rotation of the sky. Long before that, conical hats were worn by Persian Magi and Hittite kings and gods. They go all the way into the Bronze age, where such hats were made of gold and decorated with moon and sun motifs arranged into lunisolar calendars.
It is almost certain that the Ashkenazi got their Judenhuts from the Persian hats. This was not a welcome development:
...The earliest example of [Jewish dress codes], decreed in Egypt in 849 by the caliph al-Mutawakkil, required Jews and Christians to wear a yellow Persian mantle (tailasan) and a cord belt (zunnar). If they wore the Persian hat (kalansuwa) they were restricted to certain colors, and if they wore a turban it had to be yellow. Later, they also had to wear a badge of the same color. Little is known of Jewish costume in the early Middle Ages. Certain pottery figures of peddlers with Semitic features discovered in some of the Chinese T'ang Dynasty tombs (618–907) are believed to represent Jews, particularly those with pointed Persian hats, caftans, and girdles. There are no paintings or descriptions of European Jews from this period, and only two obscure references to their attire. By the 13th century, in Germany, France, England, and other parts of Europe, the Judenhut had become distinctly Jewish; it was worn voluntarily and was accepted as a Jewish symbol. Later, however, the Judenhut was also sometimes imposed by law. The hat was not worn after the 15th century, by which time a new type of hat with a tassel on its crown was prescribed.
The Persians used their hats as the basis for turbans, which were wrapped around them. The turbans have been the traditional Jewish head dress over many centuries, but then the ascendant Muslims started forbidding non-Muslims wearing them. So the Jews started going around in these Persian hats alone. Around the same time, non-ritual wearing of hats became mandatory for the Jews to distinguish themselves from the Karaites. Pointed Persian hats became to be seen in a positive light, as a badge of distinction from the heretics. Where the turbans have not been outlawed (like in Al-Andalus), pointed hats never emerged. As the Ashkenazi moved to Ashkenaz, they brought their hats with them. Soon the Europeans started to associate Jews with such hats, but there was no longer any reason for the Jews to wear Persian hats, as the turbans were considered even more of the anathema. As the Jews tried to switch to the skullcaps, the Christians took offence and forced them to wear their outmoded hats. The hats became the attribute ascribed to the Jews, the Saracens, the heretics and the witches.
The funniest thing is that coming of these cone hats from the damnation was connected with - what else - the early humanism. The 1400s were the period when the discoveries and collection of pagan artifacts gained the momentum, and the obsession with everything classical had began. It was realized that the conical hats (in the form of the Phrygian cap and the pileus) were not invented by the despised Jews, but rather belonged to the glorius European past. We can be quite certain of that because people routinely confused the two, and so the Phrygian cap was taken for the pilleum that liberated slaves wore upon their manumission. Hence the misuse of the Phrygian cap as the symbol of freedom by the French revolutionaries.
The notorious "medieval" conical hats were modern appendages, and the first documented hennin was worn in 1430 in France. The "Scholars", far from defending their use, considered such hats scandalous (Thomas Conecte required their immediate banishment and urged street urchins to tease the ladies mercilessly). The heyday of the hennin in the Northern Europe, where it was introduced quite late (circa 1500) perfectly coincided with the blossoming of Renaissance humanism, which makes the "Duns Scotus" story so delightfully absurd. As soon as the reformation and counter reformation began, the conical hats were once again banished to the eternal fire.
I am certain of their eventual comeback, given that the modern Europeans have lost none of their zeal in fighting with the headgear of religious minorities. They've been at it for 900 years, but they still cannot come to terms with our hats, as if they have no other worries in life. Fashions tend to move in circles.
We went through so many fashions since those Near East imports, to no avail... Whatever we do, they never seem to like it. Meanwhile, just because our hats (whatever they are) is the forbidden article in European eyes, they cannot help developing great lust of them. They can resist the urge for a century or two, but the forbidden fruit is sweet.
That is to say that shtreimels over hijabs would look lovely on the Burgundian dames of year 2300.
Blessed be the one who crowns Israel with glory.