Today we are going to conduct a hands-on session on how Gedmatch Oracle calculators work.

In Gedmatch you can find may calculators that return an Oracle of populations. As you have seen in the previous example, after entering your kit number and receiving the results in % format and a pie chart, you have a button called Oracle and Oracle 4 where you get an approximation of populations in combinations of 1, 2, 3 and 4 populations.

### Oracle 1 Population of Eurogenes K15

Without going into deep math details, I am going to explain how works the calculation of the oracle one population.

For this, we will see what is a distance Euclidean and Manhattan, with respect to the populations of the spreadsheet that the calculators offers next to the Oracle and Oracle 4 button.

In this screenshot, you see that there are a series of populations with a percentage distribution of weights per component K.

Given this, if we want to compare ourselves with these reference populations and see how close we are from each of them (distance), we can calculate the Euclidean distance (used by Gedmatch) or Manhattan for this purpose.

### Euclidean Distance

This formula calculates (used by Gedmatch) a distance by the sum of the difference between the percentage that it gave us in each of the 15 components and those of the reference population and then carrying out the square of the previous subtraction and finally carrying out the square root of the sum of the differences.

### Manhattan distance

We can alternatively use the distance Manhattan would apply this formula (this is not used by Gedmatch). That tries to extract the sum of the absolute values of the difference between each component.

The result for each comparison between our result and the population of the Spreadsheet will give us a distance, being closer to 0 closer = greater similarity.

If we apply it to the entire spreadsheet of the K15 we get 206 distances. If we sort it ascending, we get the Oracle 1 results as Gedmatch returns. Pretty simple.

### Conclusions

As you can see, basic mathematics can give us relatively interesting details of our DNA inheritance.