Previously I looked at the number of times different 4-digit sequences of numbers starting with ‘1’ appear in English-language books published in the year 2000. I took statistics from Google and looked at the number of times the digits ‘1491’ appeared versus ‘1492’. Obviously not all 4-digit numbers are references to years, so I simply dropped numbers that are evenly divisible by 10.
Google offers statistics for books published in a variety of languages, so I have repeated my analysis using values from the German-language books that Google has scanned.
The graph below shows the frequency of 4-digit numbers in German-language works. Number after 1700 are much more frequent than those before 1700, so to make things easy to read, I have put the y-axis on a logarithmic scale.
As in the case with English-language books, some values make a little blip on the graph. ‘1648’ is more common than ‘1647’ or ‘1649’, probably because that was the year that The Thirty Years’ War ended. (The number ‘1618’ is more common than ‘1617’, but for some reason ‘1619’ is more common than either ‘1618’ or ‘1617’.)
I have marked some other numbers that look interesting. Some are easy to explain, but others are not.
For example, we see ‘1492’ again, though it is much less prominent than was the case for English-language books. Some other numbers that are common in English-language books are also hard to see here – ‘1066’, for example’, and ‘1776’. Some others that I would expect, like ‘1517’, the year that Martin Luther started the Protestant Reformation, and ‘1989’, the fall of the Berlin Wall, do not stand out either.
Some of the values are difficult to understand their importance, like ‘1408’ and ‘1711’. I don’t know anything important that happened in central Europe in those years. In fact, all of the 1700s seem to be a time when nothing important happened in German-speaking lands, which I find strange given that it was the time of Bach, Mozart, Euler and Goethe. But ‘1848’, a year of revolutions in much of Europe, including Germany, is easy to see, as are ‘1789’ and ‘1815’.
In numbers that start with ’19’, important ones obviously include ‘1914’ and ‘1918’, which were the start and end of the First World War, ‘1933’, the year that the Nazis came to power and of course Germans are interested in ‘1945’, which is famous for being the last year that the Cubs made it to the World Series.
Overall though, I find it rather depressing how many of the references, like with English-language texts, seem to be to wars and revolutions.
I saw this post ‘The Equation that Governs Your Sales Team’s Effectiveness‘ by Thomasz Tunguz. It is not a very long read, but every sentence is dense with details, so it provides a very good list of factors that affect ‘Sales Velocity’, or the rate at a sales team can deliver money.
The basic argument is that the Sales Velocity depends on the amount of possible sales in progress (or, ‘Work in Progress’) and the Sales Cycle (the time it takes to close a sale). If there are 20 possible sales contracts being negotiated and it takes 30 days to close a contract, then on average, 20/30 or about 0.66 contracts will close every day. If 20% of those closings are sales (the ‘Win Rate’) and each sale brings in $15,000 (‘Average Price’), then the Sales Velocity is: Work in Progress x Win Rate / Sales Cycle x Average Price.
For these figures, we would expect the ‘Sales Velocity’ to be 20 x 0.2 / 30 x $15,000 = $2,000 per day
What happens if the Sales Cycle (the time it takes for the buyer to make a decision on whether or not to sign the sales contract) drops from 30 days down to 20?
In that case, the ‘Sales Velocity’ to be 20 x 0.2 / 20 x $15,000 = or $3,000 per day. By making the Sales Cycle shorter, the Sales Velocity goes up.
This all seems very straightforward, but as Mr. Tunguz points out, “these numbers don’t move in isolation; they are not independent”. To see how that might work, I made a more-detailed simulation of the Sales process dynamics using a piece of software called STELLA.
Conceptually, I think of the flow of money to be like the flow of water through a pipe. I have shown Mr. Tunguz’s Sales Velocity as a pipe in the diagrambelow. The ‘Sales Velocity’ depends on the ‘Average Price’ (in dollars per sales contract) and the rate of ‘signing Contracts’ (which is the remainder of his equation: ‘Work in Progress x Win Rate / Sales Cycle’)
I think of the ‘Work in Progress’ (the number of possible sales contracts that are being negotiated) as a bucket, represented by the rectangle. There are only two ways to get out of the that bucket – have the customer say No and flow out through the ‘losing Contracts’ pipe or have the customer say Yes and flow out through the ‘signing Contracts’ pipe’. The rate of ‘closing Work in Progress’ is the amount of Work in Progress divided by the Sales Cycle and the rate of signing Contracts and therefore, the rate of losing Contracts, both depend on the ‘Win Rate’.
Now we have a more-detailed, more kneebones-connected-to-the-thighbone operational model of what is going on an how all the big pieces are connected. I ran a simulation using a value of ‘Sales Cycle’ of 30 for the first 20 days. We can see that the Sales Velocity is $2,000/day. At Day 20, the value of ‘Sales Cycle’ drops to 20 days. That is, the account executives get faster at closing (both winning and losing contracts).
We can see that the Sales Velocity jumps up to $3,000 per day… but just for one day! It slowly drops back to $2,000/day by Day 90.
Even though the Sales Cycle is permanently shorter, the effect of the shortening quickly wears off. What is going on here? When we shorten the Sales Cycle, the flow rates out of ‘Work in Progress’ get faster (there are more contracts won and lost each day). But, the rate at which the Sales Development Representatives deliver leads (‘developing Work in Progress’) does no change. Higher out-flows from the bucket but the same rate of adding new work to the bucket means that the total amount of ‘Work in Progress’ must drop over time.
Shortening the Sales Cycle without adding more SDRs (or increasing their per-person productivity), means that the effect on the Sales Velocity will be short-lived.
Mr. Tunguz lays out all sorts of other scenarios (“increasing the average price”, “seasonality”, “company maturity”) that are too complex to deal with right here, but the simulation I have made could be the basis for exploring the ramifications of those in greater detail.
I saw this fascinating article from Science Magazine, ‘Slaughter at the bridge: Uncovering a colossal Bronze Age battle’, about an archaeological dig in northern Germany that seems to have been the site of a pre-historic battle.
I thought that the bronze ring in the center looked very nice:
I used hollow tubing, since I did not have any large-gauge solid round wire on hand. It was simple to make, but it did not occur to me until after I had fashioned it that I had made it backwards – If you look closely, it is actually the mirror image of the one in the article. I am left-handed and just made the ring the way that feels most natural to me, so this makes me think that the person who made the original might have been right-handed.
I have used the same design concept here as with the silver cup and reliquary pendant. This is a kiddush cup – a cup used by Jews to celebrate Shabbat. I am becoming increasingly interested in the use of silver for religious purposes. This is the first kiddush cup I know of based on a Catholic reliquary.
For decoration, I used an old gold ring that I bought at jeweler’s shop and then hammered into a large enough size to fit around the perimeter.
In designing this cup, I learned that Jewish religious law requires a kiddush cup to be at least one revi’it in volume, though there seems to be disagreement as to how large this is. The minimum size, according to Wikipedia, seems to be 90.7 ml and I wanted to keep it as small (and, therefore, simple) as possible, so that is the size I aimed for.
To work out the size and proportion, I made a variety of paper prototypes. If you look closely, you can see the kiddush cup and the previous smaller silver cup I made in there too.