If you want to find academic sources arguing against the possibility of measuring and confirming synesthesia or denying its existence, you'll want to dig back to the 1970's. It's not a tenable position in the 21st Century.
Eagleman DM, Kagan AD, Nelson SN, Sagaram D, Sarma AK (2007). A standardized test battery for the study of Synesthesia. Journal of Neuroscience Methods. 159: 139-145
Ward, J., Simner, J., Simpson, I., Rae, C., Del Rio, M., Eccles, J. A., & Racey, C. (2024). Synesthesia is linked to large and extensive differences in brain structure and function as determined by whole-brain biomarkers derived from the HCP (Human Connectome Project) cortical parcellation approach. Cerebral Cortex, 34(11)
Tomson SN, Avidan N, Lee K, Sarma AK, Tushe R, Milewicz DM, Bray M, Leal SM, Eagleman DM (2011). The genetics of colored sequence synesthesia: Suggestive evidence of linkage to 16q and genetic heterogeneity for the condition. Behavioural Brain Research. 223(2011):48-52
Tomson SN, Narayan M, Allen GI, Eagleman DM (2013). Neural networks of colored sequence synesthesia. Journal of Neuroscience. 33(35):14098-106.
> unfalsifiable (or often unmeaningful) inner states
One of the great things about Synesthesia is that it is one of those places where we have in fact been able to study some really interesting things about perception by connecting it to external objective measures.
We've been able to do this most of all with psychophysics testing, but in recent years we have also been able to connect this with genetics data and neural data via fMRI.
- Synesthesia is not rare. You probably know someone that has synesthesia, even they haven't mentioned it.
- There are many forms of synesthesia. Many documented forms that we know of, and very probably a bunch we haven't documented yet.
- There are cases of tasks where we are able to measure enhanced performance of that task by synesthetes. (2)
- While some synesthetes do have a single form of synesthesia, it is common for synesthetes to experience multiple forms. We've found cluster groups where subjects with a given form are more likely to have another form within the same cluster.
From the other writings on the OP's site, we can see that they report to have at least two forms of Colored Sequence Synesthesia: Grapheme -> Color, and Day of the Week -> Color.
Their report of their experience in the linked article sounds like possibly Shape -> Motion. This is a form they could have, and it's plausible that someone already known to be a multiple synesthete might also experience this.
It is also plausible that someone with a Shape -> X type of synesthesia would be able use that to spot the odd shape out faster than others.
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(1) I maintained the online synesthesia battery for a number of years while working in the Eagleman Neuroscience Lab at Baylor College of Medicine
(2) Some of these are ones that allowed us to study synesthesia on a larger scale by testing online! Among those, one particularly notable form of test is Stroop Interference. Genuine synesthetes are able to respond much faster and more accurately, and we get a good clear separation between them and controls.
Back when I was handling it, we were still using Flash for most of the interactive tests, because that was how you had to do it when it was first built circa 2007. Obviously those would have had to be redone in HTML5 since then to keep it working on modern browsers.
People have tried to define and measure this and related ideas in different ways, and I'm not sold on any of them in particular. I can however suggest some languages that stand out in some of these explorations that you might consider.
+ Lisp dialects. In particular, take a look at Clojure, Shen, and Racket.
+ Smalltalk. Try Pharo. Check out some YouTube videos with Alan Kay.
This company is an inspiration. Pulling in $10 per user per month for an application specific tiling window manager. Kinda makes you want to start a SaaS company.
