Part of Reality Cannot be Perceived

[Jim__]

5. We don't understand enough about human ideas to reach any conclusions about alien ideas.

For instance, you say:

When alien mathematicians in other galaxies have occasion to refer to the number 3.141592..., they aren't considering the simple idea of a circle that naive people think is available to almost any intelligent being in the universe. No, there aren't any ideas. Those aliens are studying the electro-chemical processes in human brains. We the people of the planet Earth pwn the realm of ideas.

But, we can find human intelligence that sees pi very differently from the way most of us see it. Daniel Tammet is a savant, he sees pi as a landscape. From wikipedia :

Tammet's unusually vivid and complex synesthesia has been widely reported. In his mind, he says, each positive integer up to 10,000 has its own unique shape, colour, texture and feel. He can intuitively "see" results of calculations as synaesthetic landscapes without using conscious mental effort and can "sense" whether a number is prime or composite. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and pi as beautiful. The number 6 apparently has no distinct image yet what he describes as an almost small nothingness, opposite to the number 9 which he calls large and towering.[8][14] Tammet has described 25 as energetic and the "kind of number you would invite to a party".[15] Tammet not only verbally describes these visions, but has also created artwork, including a watercolour painting of pi.

Tammet holds the European record for reciting pi from memory to 22,514 digits in five hours and nine minutes on 14 March 2004.[16] Tammet's record currently ranks 6th in the world.[17]

Tammett can also talk about the digits in pi but that may be because he lives around people who refer to those digits and he is able to do the translation. How do we know that an alien intelligence won't see things more the way Tammet sees things and do computations as some form of blending landscapes? I don't believe we can know that.

I don't believe that you can claim human ideas are definitely other than some neural networks in the brain that represent knowledge. Saying this does not eliminate the possibility that non-human civilizations could have knowledge of pi; it's just that their mental representation of it may be quite different than ours.