Thank you James for responding! You were my first subscription and because of your announcement of Numberphile, I now enjoy channels (many of which are Brady's) that fuel my enthusiasm for maths and science. Thank you so much!
There is a really nice Chrome extension called "Games of Life" that allows you to play with the age old simulation. It's nice because it allows you to change the rules of the environment and when you do so, you start seeing these interesting very organic patterns and systems. Many of those patterns resemble for instance the waves on cows phenomenon and it's really interesting to see that all arise from math and a bunch of simple rules.
I have a PhD in mathematics, in something called Group Theory (the study of symmetry) - which happens to be the right sort of mathematics to break Enigma in WWII. Thomas also has a PhD in mathematics, in these sort of Turing patterns. I'm sure he'll pop in and answer people's questions too.
The following link contains a paper which tries to model butterfly wing disk patterns through Turing patterns, but also gives alternative hypotheses as well math.sci.hiroshima-u.ac.jp/hmj/v32.2/ P325-336.pdf
I would of liked to hear more on examples where diffusion and chemical reactions produce unstable states. It's nature was glossed over, and I don't understand HOW it goes about it.
The problem was set by German mathematician David Hilbert at the turn of the 20th century. I believe German was used more in scientific papers than it is today. So the name of the problem stuck. It's called the Decision Problem in English, and the Halting Problem is a (counter)example to the Decision Problem.
would it be theroetically possible for me to, say, put squash into water, stir it, and caome back to it later to find it has separated into clusters of squash?
I would love to hear more about your degree and what it allows you to do. I'm very interested in hearing more specifics of what Group Theory is. Do you have any previous videos where Group Theory was applied, but you didn't explicitly state it? A video about that would be awesome, but only if you feel it worthwhile. Anyway, I love all of your videos and thanks for making them.
Good question. The answer lies in the fact that different forms of the morphogenesis model are used for different species. Thus, it is is wrong to thing about cows being much larger than butterflies therefore they should be much more patterned. It is much better to say that cows and butterflies are completely different and so we should expect to apply Turing's theory in different ways.
Except....those instances of morphogenesis which ARE fairly well worked out at present don't at all work by Turing's idea. See the wikipedia article on Drosophila embryogenesis for elaboration.
Question: Woolley said if the animal was very small it'll be all one colour... What about butterflies? Their wings display one of the most complex and intricate patterns in our natural world! Where do they fit into this? Just curious :) xxx
Well that provided a huge number of examples in nature... However he never really explored how the mathmatics was applied. Clearly this HAS to be an iterative process. What I want to know is how these simulated patterns were actually generated. Source code would help. How would I simulate my own pattern? I found some software called MClone, but it doesn't sound like the reaction-diffusion model described here, (though it gets results)
The process is indeed iterative as it evolves over time. The best start to creating the patterns can be found by following the steps on my blog: laughmaths.blogspot.co.uk/2011/06/mathematical-biology-turing-patterns.html not only do I introduce a piece of software you can use but the supplementary information to the mathematical paper I reference also includes all the gory mathematical detail.
Don't neglect to say what needs to be said just to tip toe around a shrinking breed of people. And I don't even blame them, it's just how they were brought up and now with time we're becoming a more tolerant society. Never look back.
This is a really strange theory of how animal patterns arise. It also seems to have no evidential basis. I can come to two conclusions: either this is just an analogy that I didn't get through the course of the video, or you shouldn't let mathematicians try to solve questions of such distant disciplines as biology.
I firmly recommend the video by Philip Maini: ua-cam.com/video/pN8tVldm6QY/v-deo.html&feature=related its a bit longer (45 minutes) but goes into much more detail.
Turing, you damn genius. I just saw a clip of a salamander growing from a single cell doing a lot of this stuff he was talking about ua-cam.com/video/SEejivHRIbE/v-deo.html
Thank you James for responding! You were my first subscription and because of your announcement of Numberphile, I now enjoy channels (many of which are Brady's) that fuel my enthusiasm for maths and science. Thank you so much!
There is a really nice Chrome extension called "Games of Life" that allows you to play with the age old simulation. It's nice because it allows you to change the rules of the environment and when you do so, you start seeing these interesting very organic patterns and systems. Many of those patterns resemble for instance the waves on cows phenomenon and it's really interesting to see that all arise from math and a bunch of simple rules.
I have a PhD in mathematics, in something called Group Theory (the study of symmetry) - which happens to be the right sort of mathematics to break Enigma in WWII. Thomas also has a PhD in mathematics, in these sort of Turing patterns. I'm sure he'll pop in and answer people's questions too.
The following link contains a paper which tries to model butterfly wing disk patterns through Turing patterns, but also gives alternative hypotheses as well math.sci.hiroshima-u.ac.jp/hmj/v32.2/ P325-336.pdf
I give lots talks in London, it's the open bit that doesn't seem to happen often - I'd rather they were open!
I would of liked to hear more on examples where diffusion and chemical reactions produce unstable states. It's nature was glossed over, and I don't understand HOW it goes about it.
In my heart this will be its name.
The problem was set by German mathematician David Hilbert at the turn of the 20th century. I believe German was used more in scientific papers than it is today. So the name of the problem stuck. It's called the Decision Problem in English, and the Halting Problem is a (counter)example to the Decision Problem.
would it be theroetically possible for me to, say, put squash into water, stir it, and caome back to it later to find it has separated into clusters of squash?
Coming to see your lecture at science week!
I would love to hear more about your degree and what it allows you to do. I'm very interested in hearing more specifics of what Group Theory is. Do you have any previous videos where Group Theory was applied, but you didn't explicitly state it? A video about that would be awesome, but only if you feel it worthwhile. Anyway, I love all of your videos and thanks for making them.
Good question. The answer lies in the fact that different forms of the morphogenesis model are used for different species. Thus, it is is wrong to thing about cows being much larger than butterflies therefore they should be much more patterned. It is much better to say that cows and butterflies are completely different and so we should expect to apply Turing's theory in different ways.
Could somebody point me in the direction of the "zombie video" they talked about, at the start? (about 0:10 and forward)
Except....those instances of morphogenesis which ARE fairly well worked out at present don't at all work by Turing's idea. See the wikipedia article on Drosophila embryogenesis for elaboration.
@HairyPotter2006 It's fine to he rest of us, you should check your headphones/speakers/sound card/ sound settings :)
Question: Woolley said if the animal was very small it'll be all one colour... What about butterflies? Their wings display one of the most complex and intricate patterns in our natural world! Where do they fit into this? Just curious :) xxx
Interesting stuff!
JAMES GRIME IS BACKKKKKKK
Certainly. Should anyone have any questions I'll do my best to answer them.
holy **** you responded. Thank you James!
Dr james grime is cool, by chance do you do open talks in universities/colleges in london
Well that provided a huge number of examples in nature...
However he never really explored how the mathmatics was applied.
Clearly this HAS to be an iterative process. What I want to know is how these simulated patterns were actually generated. Source code would help. How would I simulate my own pattern? I found some software called MClone, but it doesn't sound like the reaction-diffusion model described here, (though it gets results)
more volume please!
Yay!
Finally, a real video
Can you tour the country performing tapir impersonations? This would please me greatly.
The process is indeed iterative as it evolves over time. The best start to creating the patterns can be found by following the steps on my blog: laughmaths.blogspot.co.uk/2011/06/mathematical-biology-turing-patterns.html
not only do I introduce a piece of software you can use but the supplementary information to the mathematical paper I reference also includes all the gory mathematical detail.
Very insightful!
Don't neglect to say what needs to be said just to tip toe around a shrinking breed of people. And I don't even blame them, it's just how they were brought up and now with time we're becoming a more tolerant society. Never look back.
what's the mathematics behind it?
its been a long time since your last video!! you post videos more frequently on numberfile... :(
Wait, didn't he just make a video campaigning about Alan Turing?
This was it :)
Thank you :)
What I think they meant by "hate" is that the man was just so annoyingly brilliant, and it is pretty much impossible to measure up to him.
when i think james grime, i think Dr. Who...when i think of Dr. Who, the first person i think of, is James... anyone else get this feeling??
I love the cymbal clip from Living is a Problem haha
2:16, I waved back to the guy in the background...
This is a really strange theory of how animal patterns arise. It also seems to have no evidential basis. I can come to two conclusions: either this is just an analogy that I didn't get through the course of the video, or you shouldn't let mathematicians try to solve questions of such distant disciplines as biology.
cool channel.
thanks for enlightening me, i stare at my dog all day wondering why he gets those stripes, i can take him off the operating table now :D
Later they went on to find that our universe is the fir pattern on an aging sedenion cow.
Why does it matter if they're offended? If no one ever offended anyone, there would be no progress.
8:04 A real "bombe"-shell indeed
I firmly recommend the video by Philip Maini: ua-cam.com/video/pN8tVldm6QY/v-deo.html&feature=related its a bit longer (45 minutes) but goes into much more detail.
@HairyPotter2006 IlSounds fine to the rest
Hats off to the Tapir, Badger and Zebras.
From one genius, Turing, to another: Bill Bailey. watch?v=P501H4HAtFg
you could grow 5-7 finger plants
Turing, you damn genius. I just saw a clip of a salamander growing from a single cell doing a lot of this stuff he was talking about ua-cam.com/video/SEejivHRIbE/v-deo.html
Damn thats sick, see how the diferent parts exist out of generally nothing much
2:18 *waves* Hello!
Please rename this, "Why I hate Alan Turing and you should too" :D
Haha cool video