I'm interested as well in implementing Conway's Game of Life but I wonder, what are the applications of this system in computation? Can a Turing Machine be constructed with this system?
Not only is the answer "Yes, a Turing machine can be constructed out of GoL, demonstrating that GoF is universal," but given that GoL is itself a computation, the reverse is true: You can build GoL out of a Turing machine.
I took a stab at it a few years ago. My strategy was to start with a very basic Turing Machine, and then write a compiler that compiled a more sophisticated Turing Machine out of a simpler Turing Machine.
For example, when I wanted cells to have a value and a tag, I wrote a compiler that translated every possible combination of symbol and tag into a single flat space of symbols.
I stacked compiler on top of compiler until I had a Langdon's Ant with various programming conveniences, and I wrote a 9-cell GoL using my Langdon's Ant.
The whole thing compiled to a very simple TM with millions of states, but it worked. I did not make it practical enough to ever manage a GoL big enough to emulate a Turing machine, but I feel that I did enough to get some practical experience with something that is straightforward in theory.
> what are the applications of this system in computation?
If you mean "applications" in the practical sense, there are basically none, but that's part of the fun. GoL is fascinating in part because it's pretty much useless, yet has been studied extensively by bored computer scientists over the decades.
> corona: "crown" (from latin corōna, meaning "crown")
> virus: "poisonous secretion" (from latin vīrus, meaning "venom" or "poisonous secretion")
> Coronavirus, the virus responsible for 30% of common colds, as well as SARS, has the appearance of a crown (corona) under electron microscopy, due to the spike proteins that coat the viral surface. Viruses, being so small, might have been thought of before they were discovered, to be poisonous secretions (virus) of unknown origin, hence their name.
It is unrelated but the mechanism by which the association came about is funny: it was first widely (read: honestly) reported by Spain, therefore everyone associated it with Spain, even thought first cases, including initial deaths, were in other countries which suppressed the news.
In fact, the only relationship that virus had with Spain is that the press was not censored as in the other European countries of that time (because of their involvement in the Great War).
I think A Mathematician's Apology is a good read, but if you're looking to learn mathematics there are probably better places to start.
If you want a cursory view of various parts of mathematics, you might prefer Courant's book "What is Mathematics?". Depending on your background and interest, there is a volume of books (available as a consolidated cheap Dover paperback) called Mathematics: Its Content, Meaning, and Methods.
I recently came across A Programmer's Book of Mathematics[0] -- I haven't read it, but the author is a developer and the content might be more appropriate if you're just starting out -- both of the other books I mentioned are older, and are really wonderful texts, but might possibly be overwhelming depending on your appetite and background.
Finally, if you're more interested in math that's relevant to software engineers, there's Knuth's book "Concrete Mathematics".
I'd second the "What is Mathematics?" and "Mathematics: Its Content, Methods and Meaning" recommendations, in that order. Both are very cheap, comprehensive, and in ascending rigour. After those, it's really dealer's choice, with "Concrete Mathematics" being of particular interest to computer scientist.
Additionally:
- "Princeton Companion to Mathematics" is really fun to have around for exploration
- if you're really really rusty with math, take a week or two with "Mathematical Handbook - Elementary Mathematics" by Vygodsky
I literally have all these on my desk at this very moment, what a fun coincidence.
No. It's been a while since I read it, but I found it an unapologetic, tedious, arrogant, self-serving screed lionising pure mathematics (and its practitioners, but only the very best), denigrating anything applied or even applicable, yet basically asking the hoi polloi doing that nether pedestrian work of actually working to put food on his table.
And, it's not even particularly good in instilling some appreciation of the beauty of mathematics.
It's not much about maths, it's a memoir by a particular mathematician written at an unhappy point in his life, reflecting back on what he has done. It belongs more to the literature about artists and creativity, than to books of mathematical content. For that, see instead Hardy's Course of Pure Mathematics [1]
If you do read the Apology, be sure to get an edition with C.P. Snow's forward, which gives the back story that puts Hardy's memoir in context. It also includes the wonderful story of Hardy and Ramanujan.
It's a great read. I have also found a great reading list of from the University of Cambridge[0] that has a whole different range of books and websites for those who have a cursory interest in Mathematics.
I would suggest picking up a textbook in mathematics for a specific area relevant to your interest.
I found that studying specific topics (currently probability theory and statistics) helped me comprehend the field better and in ways that make it practical for my planned career.
I think that "not caring about other people actions" should be the standard way of thinking if you think their actions doesn't cause harm to other humans. That's what I get from that text.
But he already said he had a problem with inhumanely produced meat, in other words, actions that cause grave harm to animals. Why would you have that standard at all if you don't care if it's met?
(There's also the land use and emissions angle. Arguably meat consumption causes harm to all humans and beyond.)
For me, it’s a “chose your battles” sort of thing. I don’t seek confrontation nor even diminishing others. Life is too, too short. I further hope that my nonviolence will lead others to treat me nonviolently.
But is the parent really needed here? This discussion seems to have become "how dare you take a stance in this issue that we cannot fully understand"?
How about, while hungry they are sickened by the cruelty involved in producing food, but while full, they simply have other, more important things on their mind?
I don't care that much about animals, as far as their pain or feelings.
If we slaughter ants and fruit flies while not caring for their rights, what is that different from a cow or dog?
I know this is an unpopular position, but I don't see the logic in animal rights.
Now, when we're talking about maintaining ecosystems, I'm all for it. What's happening to bees is bad for humans.
But creating cattle just to slaughter and eat it, that's just part of our nature. Like a lion slaughters a gazelle. We just evolved to have the tools to breed them...
Maybe cattle breeding is inefficient and pollutes the planet. That's also bad,but it's the best way we've found yet to feed billions of people and keep affordable food prices.
I am sure almost every action could indirectly be related to human suffering of some sort. Using a phone for example and there is a good chance that it will have cobalt mined by children in Congo.
Sure. But that's a very weak excuse if it's one at all. I sometimes jaywalk, does this justify me mudering someone? I mean I can't be perfect right so why even try?
