Also gotta shout out to these incredible molecular animations by WEHI: https://www.youtube.com/watch?v=7Hk9jct2ozY

For example, sequencing instruments include base quality strings in the output. Base qualities are estimates how likely the instrument got each sequenced base right. But most people don't want to store that much noise, especially when the actual data is highly compressible. So the base qualities get quantized using more or less principled methods that seem to work well empirically.

Read aligners make similar estimates of how likely they got the correct alignment for each read. Those estimates are typically based on simplistic models and a number of assumptions. There are two main components in the estimate. One is based on comparing the primary alignment the aligner chose to the secondary alignments it also found. Another is an estimate that the aligner didn't find the correct alignment, because that part of the sequenced genome is too different from the reference. The latter is obviously handwavy. And the aligner cheats in the former. Because people don't want to wait 10x or 100x longer for better results, the aligner gives up early and estimates how good secondary alignments it might have found if it had actually done the work.

And then there is variant calling. At some point, the state-of-the-art callers were statistical. But then people got better results with neural networks. Or at least the results were empirically better.

But they produce short reads, and because DNA is full of repetitive fragments, it's not always clear where the read came from.

We also have two copies of genes, which also further complicates matters.

The first startup where I worked, developed synthetic long reads on top of Illumina's hardware. We could stitch together 50kbp reads, which really helped with de-novo sequencing.

The DNA of a nucleated (a.k.a. eukaryote) cell is indeed split into multiple chromosomes and the number of the chromosomes and the number of genes on each chromosomes and the sequence of the genes on each chromosome are normally constant for a species and very similar for closely related species. The cells that have an incorrect number of chromosomes (which happens when a cell division does not work correctly) will normally die soon, because their DNA is incomplete.

Only when a cell has all the normal chromosomes, but also some extra chromosomes, it has a chance to survive, even if the extra chromosomes may interfere with some internal processes. Because superfluous chromosomes are much less harmful than missing chromosomes, there have been cases, rare at animals, but frequent at plants, when the entire genome has been doubled, when some cell division has failed, but the descendants of that cell have survived.

There are animals for which the number of the chromosomes and the sequence of the genes on them has remained unchanged for many hundreds of millions of years, though there are also animals where the DNA has been completely rearranged, because some chromosomes have fused into a single chromosome, other chromosomes have split into multiple chromosomes, and on some chromosomes the genes have been shuffled.

Nowadays, it is known that it is very likely that the common ancestor of all animals except comb jellies had 29 chromosome pairs (humans have 23 pairs). In most animal branches there were more chromosome fusions than chromosome splittings, so in the present most animals have fewer than 29 chromosome pairs.

Among the animals with the most conservative genomes are some sponges, some jellyfish, many echinoderms and some of their relatives, i.e. acorn worms, the lancelets, some nemertean worms and some bivalves.

There's the X and Y chromosomes, those produce a binary result (unless you have a genetic anomaly). And after that comes the messy and fuzzy parts I mentioned, where those genes trigger changes in hormone levels and development. And those parts are analog, very complex and contain a lot of different parts. So the outcome is not binary anymore.

Meanwhile human geneticist doesn't even need to collect any data. Reference genomes are always being improved. People dump their data into public repositories (at least public for other credentialed researchers). A couple emails and filling of approval forms and you too can have access to 10,000 patient samples of some human disease already sequenced for you to an acceptable depth. Of course you will still need to pay for downstream compute needs in money and your time crafting the analysis to suit your reasoning, but still, half the battle is already won when you work on these well trodden paths. So much necessary groundwork has been performed by others for you already.

There are more combinations than merely having only X, or an XY combination. And there is more fuzziness even in the Y and X expression, as you said. It's fuzzy all the way down. The tale of Binary results has always been from compression of reality: Always has been.

But you're right, the full range of biological possibilities is very fuzzy . SRY itself a just a regulatory switch that other sex-linked traits are conditionally dependent on. If the switch gets broken, you develop as female. If genes that support the switch break, you might develop as female. If a sex-linked trait downstream from SRY mutates, then pretty much anything can happen. And other species do sex determination completely differently. Hell, a lot of bacterial sex basically involves throwing pseudo-viruses at each other.