A Prime Surprise (Mertens Conjecture) - Numberphile

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From: Numberphile
Duration: 09:56

Dr Holly Krieger discusses Merterns' Conjecture.
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More links & stuff in full description below ↓↓↓

More videos with Holly (playlist): http://bit.ly/HollyKrieger

Dr Holly Krieger is the Corfield Lecturer at the University of Cambridge and a Fellow at Murray Edwards College: https://www.dpmms.cam.ac.uk/~hk439/
On Twitter: https://twitter.com/hollykrieger

PAPER: Disproof of the Mertens Conjecture: http://www.dtc.umn.edu/~odlyzko/doc/arch/mertens.disproof.pdf

More on Mertens Conjecture: http://mathworld.wolfram.com/MertensConjecture.html

Useful OEIS sequences:
https://oeis.org/A002321
https://oeis.org/A084237

Holly on the Numberphile Podcast: https://youtu.be/QmfQQzjpdpM

The Riemann Hypothesis: https://youtu.be/d6c6uIyieoo

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

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jlvanderzwan
3 hours ago
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What have you been up to, Meerten?
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Don't Blame Gwyneth For Goop's Success

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From: Medlife Crisis
Duration: 10:20

Goop deserve all the criticism that's been flying their way but to *only* concentrate on them is to miss the reason snake oil wellness peddlers like goop and charlatans like chiropractors are doing so well. The modern medical system is failing a lot of people.

I'm not suggesting for a moment that those highlighting the pseudoscience and danger of goop are wasting their time - especially ahead of Netflix's disappointing decision to air 'The Goop Lab', which will spread goop's BS yet further. I believe we should challenge bad science wherever we see it. I am just providing a slightly wider picture to explain why alternative medicine continues to enjoy success despite so many wonderful advances in actual medicine.

I'm a practicing doctor and like almost all my colleagues, there are many aspects of modern medicine that frustrate me. This channel deals with a lot of them. I believe we need to spend as much time turning a spotlight on the medical system as we do on the quacks and wellness gurus.

-----------------

More Medlife Crisis:

http://www.medlifecrisis.co.uk
https://twitter.com/medcrisis
https://www.facebook.com/Medlifecrisis
https://www.instagram.com/medcrisis

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jlvanderzwan
5 hours ago
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Nancy by Olivia Jaimes for Tue, 21 Jan 2020

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Nancy by Olivia Jaimes on Tue, 21 Jan 2020

Source - Patreon

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jlvanderzwan
1 day ago
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I wonder how many parents feel like this one is getting a little to real
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the stareTumblr — Twitter — Facebook — Instagram — Buy my books...

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the stare

Tumblr TwitterFacebookInstagramBuy my booksSupport me on Patreon

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jlvanderzwan
1 day ago
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Modern horror
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diy#08 touchpad for c64 and pc

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From: janderogee
Duration: 08:02

This video is about the commo pad project. The commo pad is a touchpad based device for your C64. It is made to act like a KoalaPad, 1351 mouse, or a joystick. It can also connect to your PC and act like a normal 2 button mouse with scrollwheel.

For more information regarding this project, visit my website:
http://home.kpn.nl/bderogee1980/projects/COMMO_PAD/COMMO_PAD.htm

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jlvanderzwan
3 days ago
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Let’s have some fences!

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Fences have been long on the game’s todo list. Being a really neat feature described by a single word, it comes with a lot of problems to solve. How does one approaches a feature like that?

First the “wants” had to be outlined. Fences might have a number of variants and uses in the game:

  • Short crossable fences can be used to designate grain fields and orchards. Purely aesthetic
  • Medium breakable fences. Can be a weak fortification, slowing down enemy advance. Maybe they can also be used to keep the cattle
  • Tall tough fences can be a better fortification. More expensive and harder to break
  • If we think about it, fences around house building sites are somewhat related too

Next comes the problems and features exploration phase. Here’s a short FAQ I did on fences before starting the work. Each line poses a problem and has a solution below. The FAQ is not final and solutions can be changed to accomodate for unforeseen problems, but for now I’m quite happy to have most of the questions answered:

  • How are fence plans placed
    • New plan type. Placed between tiles. One side must be walkable/reachable. Cursor magnets to nearest edge and outlines it.
  • How fences get built
    • By builder. He arrives on adjacent tile, digs for a while, waits for timber and hammers the fence in place
  • What do fences cost 
    • At least one wood or stone
  • On which side of the fence should the builder remain?
    • Let the fence plan direct from which side it gets built
  • Do builders walk through fences?
    • Maybe they don’t. Let the player manage the sides from which to build.
    • We could allow Builders to walk through fences. But this would break all the immersion and logic. Unless we show Builder hits a fence several times to remove it, walks though and then builds it back again? Builders do walk through small house plan fences though..
  • How fences get demolished?
    • Instantly in a puff of dust
  • How fences get destroyed?
    • Adding hp would be complicated. Let it be just a chance-based instant destruction. 
    • Maybe we can have a breaking animation and fence remainders on the ground?
  • How tough are the fences?
    • We can “roll dice” each hit. Chance of destruction can be linked with warriors attack.
  • How do we discourage extensive fortifications, are they a problem?
    • Likely not. The cost is quite high after all.
  • Whose property fences are?
    • Fences belong to a player (so warriors know whose fences to break and whose to walk around)
  • How do fences interact with houses?
    • Fences should be allowed to make perpendicular contact with houses
    • Fences could be allowed to go alongside house border later on, but likely it ’s not needed
  • How to build fenced area for cattle?
    • To become cattle yard it needs to be enclosed
    • Area can be built by builders
  • What is a yard?
    • Any enclosed area of size 4+ touching the house (e.g. side). Max size is .. ?
  • How do animals appear inside the yard
    • Breeder can bring them from the house
  • How do animals disappear from the yard
    • Breeder takes them out
  • How does Breeder carry the animal?
    • Animal goes by itself on a whistle?
    • Animal gets “follow” order?
    • Animal is taken into hands? (as in KaM) 
  • What if fence gets broken?
    • Yard becomes ordinary terrain
    • Animals can walk away
  • What if fence gets restored (or is built around existing animals)
    • Area becomes yard again
    • Breeder can access animals in the yard
  • What if player builds several yards
    • If they are accessible by Breeder – he can use them
  • What if there are odd units/animals in the yard
    • They remain there, if they can not escape
  • How do animals breed?
    • Breeder brings them in
  • What do animals eat
    • Grass and grain brought by Breeder
  • How do animals grow?
    • Cows/Horses grow +1 for each grain eaten
    • Sheep remain at the same size and just grow more wool
  • Do we always need fences 
    • No, if the area is naturally enclosed it should be fine too

This FAQ covered the player-side of things. Having that done the coding could begin. The code was written in a separate SVN branch to allow for easier comparison of before/after and overall changes made.

There was a number of cross-dependent problems in implementing of the fences. Here are some of the solved ones:

  • Fence edges block diagonal unit passability across a vertice between tiles (just like trees and such). However a fence has 2 endpoints, so code had to be updated to let 1 object block 2 vertices.
  • Fences go along tile edges and thus block unit passability. All the passability/pathfinding methods had to be updated to check the edges between tiles for passability
  • Unlike roads and fields, fences need to be built from specified side. Fence plan list had to account for that.
  • Enemy fences should be breakable, so the passability for warriors had to “ignore” the fences and still plan paths through them, knowing that warrior will break the fence on approach.
  • Breaking enemy fences should not interrupt current warriors order
  • Warriors should not break allied fences. Which means the terrain traversability now had to account for player alliances.
  • Breaking a fence should take some time (1-3 hits depending on warriors strength). Had to come up with a simpler formula for that
  • There needs to be support for different fences (visually and mechanically) at least for mapmakers. Thus the fences are planned to have properties and types.
  • Had added dynamic script commands to add or remove a fence.
  • Fences had to have player color markings on them. Since terrain render is already overly complex and overlay render caused some Z-fighting bugs, fences had to be made to render via a different approach that allowed for colors.
  • Refactorings had to be made along the way to adjoin similar methods encountered throughout the code.

Remaining problems and features:

  • Own fences need to be demolishable. There’s still no support for that yet. Not sure if this should be done with a confirmation or not.
  • It would be nice to have own and allied fence lines to be permeable without destruction. Should the gates be added, and if yes – that’s another bunch of problems to solve
  • It would be nice to have fence breaking animation
  • Cattle yards are a whole new can of worms. They will likely be implemented as a separate feature after the fences development is complete.

Fences are available since Alpha r8455. There’s already been some testing going on and a small bunch of bugs fixed.

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jlvanderzwan
4 days ago
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Never thought fences had such far-reaching consequences for pathfinding and such
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