Sometimes I get asked if I’m related to the great physicist Ernest Rutherford. His discoveries about the atomic nucleus gave birth to physics in the 20th century. He is the father of nuclear physics, with labs and atoms named after him.

I’m not related to him. I can reveal however that I am a direct descendent of someone of similar greatness: Charlemagne, Carolingian King of the Franks, Holy Roman Emperor, the great European conciliator. Quelle surprise!

But we are all special, which means none of us are. If you’re vaguely of European extraction, you are also the fruits of Charlemagne’s prodigious loins. A fecund ruler, he sired at least 18 children by motley wives and concubines, including Charles the Younger, Pippin the Hunchback, Drogo of Metz, Hruodrud, Ruodhaid, and not forgetting Hugh.

This is merely a numbers game. You have two parents, four grandparents, eight great-grandparents, and so on. But this ancestral expansion is not borne back ceaselessly into the past. If it were, your family tree when Charlemagne was Le Grand Fromage would harbour more than a billion ancestors – more people than were alive then. What this means is that pedigrees begin to fold in on themselves a few generations back, and become less arboreal, and more web-like. In 2013, geneticists Peter Ralph and Graham Coop showed that all Europeans are descended from exactly the same people. Basically, everyone alive in the ninth century who left descendants is the ancestor of every living European today, including Charlemagne, Drogo, Pippin and Hugh. Quel dommage.

With the advent of cheap genetic sequencing, the deep, intimate history of everyone can be revealed. We carry the traces of our ancestors in our cells, and now, for the price of a secondhand copy of Burke’s Peerage, you can have your illustrious past unscrambled. Plenty of companies have emerged that provide this service, such as 23andMe and Ancestry DNA. Spit in a test tube, and they will match parts of your DNA with people from all over the world. The results are beguiling, but don’t necessarily show your geographical origins in the past. They show with whom you have common ancestry today.

People love discovering that they’re a bit Viking, or a bit Saracen. This is big business nowadays, and some companies spin fabulous yarns about your forebears as marketing devices. I’ve been making a documentary for Radio 4 on what genetics can and can’t tell you about ancestry, and examining some of the more outlandish claims that some ancestry businesses make. One company offered a service whereby it would tell you the precise village location of your genetic ancestry 1,000 years ago. It’s a peculiar thing to claim, as you will have thousands of ancestors 1,000 years ago, and I’m pretty sure they won’t have all come from the same village. Their algorithm clearly needed some work: it placed the genetic origin of one paying customer in the depths of the Humber estuary.

The truth is that we all are a bit of everything, and we come from all over. If you’re white, you’re a bit Viking. And a bit Celt. And a bit Anglo-Saxon. And a bit Charlemagne. This is not to disparage genetic genealogy and ancestry. Done right, it is an immensely powerful tool for studying families and human migrations. DNA can disclose unknown cousins or parents. Further back, the past becomes dimmer, but not invisible. A dazzling, detailed analysis of the British genome last month scrutinised the history of immigration over the past 10,000 years. Expect many more studies like this from all over the world revealing all manner of dalliances from the foggy past.

Often genetic ancestry relies on the Y chromosome, which is inherited only via the paternal line, or mitochondrial DNA, which is only passed on from mothers. These make for persuasive – but often simplistic – analyses of ancestry. These two chunks of DNA make up 2% of your genome. But the other 98% has to come from somewhere too, and that is a pick-and-mix from all the rest of your ancestors.

Each subsequent generation, the contribution from an individual from your lineage becomes less. Professor Mark Thomas from University College London describes this dilution as “homeopathic”. After a few rounds of preparation, homeopathic dilutions contain no molecules of whatever the active ingredient is imagined to be. Genetic inheritance works in a similar way. Half of your genome comes from your mother and half from your father, a quarter from each of your grandparents. But because of the way the DNA deck is shuffled every time a sperm or egg is made, it doesn’t keep halving perfectly as you meander up through your family tree. If you’re fully outbred (which you aren’t), you should have 256 great-great-great-great-great-great-grandparents. But their genetic contribution to you is not equal. Before long, you will find ancestors from whom you bear no DNA. They are your family, your blood, but their genes have been diluted out of your bloodline. Even though you are directly descended from Charlemagne, you may well carry none of his DNA.

So what does this all mean? Ancestry is messy. Genetics is messy, but powerful. People are horny. Life is complex. Anyone who says differently is selling something. A secret history is hidden in the mosaics of our genomes, but caveat emptor. If you want to spend your cash on someone in a white coat telling you that you’re descended from Vikings or Saxons or Charlemagne or even Drogo of Metz, help yourself. I, or hundreds of geneticists around the world, will shrug and do it for free, and you don’t even need to spit in a tube.

The Business of Genetic Ancestry is on BBC Radio 4, Tuesday 26 May at 11am