I learned it manually just using a checker board or chess board. To play it is this simple:

1. Start with any pattern you want of black checkers on the board.
2. Look at each block on the checker board one at a time. If the block is empty and there is exactly three black checkers surrounding it (that is in the 8 blocks adjacent to it). Place a red checker on that spot.
3. Look at each black checker on the checker board, if there is less than 2 black checkers surrounding it or more than 3 black checkers surrounding it, remove the checker from the board.
4. Replace all of the red checkers with black checkers.
5. Return to step 2 and repeat as many times as you desire.

The 'edges' of the board though does cause problems as what to to with those checkers. I think in Conway's game the board has an infinite number of rows and columns.

Obviously you cannot get to many complex patterns on an 8x8 board but it is fun for kids as it teaches patience and concentration. You can also experiment around with changing the 'rules' and see what happens.

Hi,

Sounds similar to solving some partial differential equations numerically.
In that case the edges, or just outside of the edges, are consider the boundary conditions and you would know that from the problem specification. The boundary conditions react with the inner cells (squares on the board) and that causes the changes there. The boundary conditions can be almost anything, from a constant along the sides and different constant along top and bottom, or even some derivative or some gradient along each edge.

Maybe an interesting idea might be to group several boards and have them act like a supercosm of cells. Each microcosm would have their own laws but the super set would have different laws. I guess there could be a lot of variations though.

 

Hi,

Sounds similar to solving some partial differential equations numerically.
In that case the edges, or just outside of the edges, are consider the boundary conditions and you would know that from the problem specification. The boundary conditions react with the inner cells (squares on the board) and that causes the changes there. The boundary conditions can be almost anything, from a constant along the sides and different constant along top and bottom, or even some derivative or some gradient along each edge.

Maybe an interesting idea might be to group several boards and have them act like a supercosm of cells. Each microcosm would have their own laws but the super set would have different laws. I guess there could be a lot of variations though.

Nice idea, having multiple board groups with different rules. I may consider creating another version of the game for my Windows machine similar to that idea allowing you to set the rules and experiment. At the moment I have a Windows .NET C# version that has an 'infinite' plane that follows the original rules. It may also be interesting to introduce 'fuzzy' rules where a cell can be anything from completely dead 0% to completely alive 100%.

 

Nice idea, having multiple board groups with different rules.

If this is how you enjoy spending your time, you'll want to check this out:

https://golly.sourceforge.net/

 

If this is how you enjoy spending your time, you'll want to check this out:

https://golly.sourceforge.net/

Nice! Thx.

 

Nice idea, having multiple board groups with different rules. I may consider creating another version of the game for my Windows machine similar to that idea allowing you to set the rules and experiment. At the moment I have a Windows .NET C# version that has an 'infinite' plane that follows the original rules. It may also be interesting to introduce 'fuzzy' rules where a cell can be anything from completely dead 0% to completely alive 100%.

I like that idea too.

Also, how about using two types of cells: 'rabbits' and 'foxes'. The rabbits can reproduce, and the foxes can reproduce and they eat some of the rabbits. Over time the population of rabbits grows or diminishes, and so if too many foxes come about then they eat all the rabbits and everything dies
It could also be that the populations grow and shrink but continue on.

 

I like that idea too.

Also, how about using two types of cells: 'rabbits' and 'foxes'. The rabbits can reproduce, and the foxes can reproduce and they eat some of the rabbits. Over time the population of rabbits grows or diminishes, and so if too many foxes come about then they eat all the rabbits and everything dies
It could also be that the populations grow and shrink but continue on.

Humans & flying saucers would be more fun -- the humans get to advance technologically and shoot back, all the while devolving into primitive tribal cultures.

Oh, wait. That's the sim we're in now.

 

The Most Boring Number in the World Is ...

​

So Guglielmetti went in search of really boring numbers: those that hardly appear in the OEIS catalog, if at all. The latter is the case, for example, with the number 20,067. As of March, it is the smallest number that does not appear in any of the many stored number sequences. (This is just because the database stores only the first 180 or so characters of a number sequence, however—otherwise, every number would appear in the OEIS’s list of positive integers.) So the value 20,067 seems quite boring. By contrast, there are six entries for the number 20,068, which follows it.

 

​

 

Scientists Discover 'Pure Math' Is Written Into Evolutionary Genetics

​

What's more, the maximum robustness followed a self-repeating fractal pattern called a Blancmange curve, and was proportional to a basic concept of number theory, called the sum-of-digits fraction.

 

https://www.scientificamerican.com/...-first-law-discovered-after-nearly-300-years/

In a recent paper published in the journal Philosophy of Science, Hoek argued that Newton had no intention of using the first law to refer to imaginary, force-free bodies. Newton’s use of the Latin for “except insofar” (nisi quatenus) was meant not to specify that the law referred only to such bodies, he said, but to point out that motion only changes insofar as a force compels it to. In other words, Hoek wrote, a better paraphrase would refer to all bodies: “Every change in a body’s state of motion is due to impressed forces.”
...
The confusion over what Newton meant likely persisted because of a Latin-to-English translation made by Andrew Motte in 1729, after Newton’s death, that used the word “unless” instead of “except insofar.” This was a subtle difference that nonetheless made it seem like Newton was talking about force-free bodies instead of explaining why all bodies react to forces, Hoek says. After this, people “probably, for the most part, did not go back to the original translation,” he says.

Equivalence, the expressions are the same in reality so I don't see it as meaning much.

 

Scientists Discover 'Pure Math' Is Written Into Evolutionary Genetics
View attachment 302170​

No it did not evolve to begin with. One of the most versed mathematicians David Berlinski, practically a genius considered a single cell to be more complex than a Galaxy. DNA is also an information source that uses four types of molecules like an alphabet, specifically: Cytosine, Adenine, Thymine , and Guanine. An information source cannot be created over any period of time no matter how long that time may be. It would be like taking a book and slowly scrambling the letters, the probability of losing information goes up not down. I would recommend reading the book "Darwins black box" along with "Genetic entropy and the mystery of the genome". These and other books like it demonstrate the impossibility of information slowly accumulating over time. Now before you say I am wrong, you need to at least read these and other books.

Here are some links by many other extremely intelligent people who don't even believe evolution is possible:

https://www.wayoflife.org/reports/scientists_who_do_not_believe_in_evolution.php
http://www.scienceagainstevolution.org/v5i10f.htm
https://www.quora.com/Are-there-scientists-who-refuse-evolution

Below is a link to 1000 scientist that show that:

1000 Scientists Sign Up to Dissent from Darwin

There is a saying that goes: "Beware the one hand clapping". Meaning you need to be open to the possibility that the other side is right.

I have studied molecular biology as a hobby for a long time and yes there a plenty of scientist who think it did evolve and I have looked into them and done my 'homework' and looked at both sides of the argument. Have you looked at the 'other side' (Beware the one hand clapping)? But after reading other sources, I found myself to be right: It could not evolve.

 

The famed Fibonacci sequence is but one example found in the article you referenced.
The main theme of that article being:

Scientists Discover 'Pure Math' Is Written Into Evolutionary Genetics

Is simply false.

 

A Wild Claim about the Powers of Pi Creates a Transcendental Mystery

​

The notion that raising an irrational number to multiple powers could result in a number with no numbers after the decimal point may seem far-fetched at first. But there are other examples. For instance, √2 to the power of (√2 to the power of √2) can be simplified to √2√2 x √2 and therefore results in √22 = 2. It is not so easy to see how such calculations would work with π, however.

 

A Wild Claim about the Powers of Pi Creates a Transcendental Mystery
View attachment 313575​

Hi,

There are some other interesting numbers out there like the golden ratio G. The square of G is 1+G and the reciprocal of G is G-1. 1/sqrt(G) is roughly equal to pi/4.
G is of course the number approximately +1.6180339887498948482045868343656381177...
There may be other relationships there too.

pi^3 produces an 'almost' whole number 31.00627... and can be used to create an approximation to pi itself:
31^(1/3)+1/4717
differs from pi by about -0.000000002 which would be a low percentage error.
Just have to come up with a memory device to remember that integer 4717.

Also for the example, I think it is really (sqrt(2)^sqrt(2))^sqrt(2)=2.

 

The fascination and complexity of the world's hardest math problems

​

This article will explore some of the hardest math problems ever posed and the different approaches mathematicians have used to solve these problems.

 

 

The dedication to the State Science Institute:

"To the fearless mind. To the inviolate truth."

She was right about everything.

 

Excellent video. Thanks for posting.

 

A Wild Claim about the Powers of Pi Creates a Transcendental Mystery
View attachment 313575​

See https://en.wikipedia.org/wiki/Euler's_identity

 

No it did not evolve to begin with. One of the most versed mathematicians David Berlinski, practically a genius considered a single cell to be more complex than a Galaxy. DNA is also an information source that uses four types of molecules like an alphabet, specifically: Cytosine, Adenine, Thymine , and Guanine. An information source cannot be created over any period of time no matter how long that time may be. It would be like taking a book and slowly scrambling the letters, the probability of losing information goes up not down. I would recommend reading the book "Darwins black box" along with "Genetic entropy and the mystery of the genome". These and other books like it demonstrate the impossibility of information slowly accumulating over time. Now before you say I am wrong, you need to at least read these and other books.

Here are some links by many other extremely intelligent people who don't even believe evolution is possible:

https://www.wayoflife.org/reports/scientists_who_do_not_believe_in_evolution.php
http://www.scienceagainstevolution.org/v5i10f.htm
https://www.quora.com/Are-there-scientists-who-refuse-evolution

Below is a link to 1000 scientist that show that:

1000 Scientists Sign Up to Dissent from Darwin

There is a saying that goes: "Beware the one hand clapping". Meaning you need to be open to the possibility that the other side is right. He begins by talking about the work he does, its applications to medicine, Nano machines etc.

I have studied molecular biology as a hobby for a long time and yes there a plenty of scientist who think it did evolve and I have looked into them and done my 'homework' and looked at both sides of the argument. Have you looked at the 'other side' (Beware the one hand clapping)? But after reading other sources, I found myself to be right: It could not evolve.

Here's James Tour, a scientists scientist, he knows his subject and frankly more people should listen dissenters. He starts out by summarizing the work his team does, in medicine, Nano machines etc.