As there seems to be resistance to the point that the world embeds structure and quantity (thus, mathematical features) I think it is useful to provide some simple reminders.

The Egyptian rope trick and the 3-4-5 Pythagorean triplet, thus a right angle forced through a numerical relationship (and note the power of the number twelve again):

Lego bricks demonstrating the Pythagorean relationship — notice, number theory connexions and the natural interpretation of “squaring”:

Also, notice a Mobius strip cutting exercise:

In none of these cases is the result dependent on our creating a mathematical model or an axiomatisation. The results are objective, factual, embedded in the world and in fact helped to constrain how Mathematical systems were axiomatised. **END**

In none of these cases is the result dependent on our creating a mathematical model or an axiomatisation. The results are objective, factual, embedded in the world and in fact helped to constrain how Mathematical systems were axiomatised. **END**

**PS:** Dr Tokieda’s lecture on Mobius strips (with demonstrations):

Lecture series, here.