What is the penalty for the number of cites, for science and culture?

I see on the KNOWLEDGE virtue, that "Networked datalink" and "Memeweb" reduce the penalty for number of cities for culture and science by 40%. what is that penalty anyway?

While I never cared for the specific numbers, science and culture/virtues are pretty easy to explain:

• Basically you'll need x points to complete a research or develop a virtue.
• While some means of gaining such points are global or unique (e.g. inherent to your sponsor or connected with wonders), most originate from buildings that can be built in all cities.
• Due to this, the most logical step to achieve higher levels fast, would be to just build as many cities as possible:
  • Your second city would double your output, i.e. halving the time it takes to finish science projects or develop virtues.
  • The third city would still increase that output by 50%, etc.
• To counter this, the game adds so called penalties. While I don't have actual numbers, imagine that completing a science project would take 60 science points. If you build a second city, you get a penalty and need 100 science points rather than just 60.

The whole thing can be explained with introduced overhead (let's assume scientists have to travel between cities, have to synchronize or compare their results, etc.) and it makes the whole effect far less extreme.

You still profit off your second city (assuming you build the apropriate buildings), yet it's more reasonable to avoid making it too attractive to just build cities an leave them underdeveloped. Just imagine someone establishing 10 cities with just the first few science buildings, since those are finished faster than fully upgrading just one or two cities.

The virtue mentioned by you lowers this penalty. So given the numbers above, rather than requiring 100 points for two cities, you'd just need 84 (40% less increase), making a faster expansion far more interesting.