Posts tagged as “Hard Science”
So, when I say "I teach robots to learn" ... that's what I do. -the Centaurhttps://arxiv.org/abs/1710.03937 PRM-RL: Long-range Robotic Navigation Tasks by Combining Reinforcement Learning and Sampling-based Planning
We present PRM-RL, a hierarchical method for long-range navigation task completion that combines sampling-based path planning with reinforcement learning (RL) agents. The RL agents learn short-range, point-to-point navigation policies that capture robot dynamics and task constraints without knowledge of the large-scale topology, while the sampling-based planners provide an approximate map of the space of possible configurations of the robot from which collision-free trajectories feasible for the RL agents can be identified. The same RL agents are used to control the robot under the direction of the planning, enabling long-range navigation. We use the Probabilistic Roadmaps (PRMs) for the sampling-based planner. The RL agents are constructed using feature-based and deep neural net policies in continuous state and action spaces. We evaluate PRM-RL on two navigation tasks with non-trivial robot dynamics: end-to-end differential drive indoor navigation in office environments, and aerial cargo delivery in urban environments with load displacement constraints. These evaluations included both simulated environments and on-robot tests. Our results show improvement in navigation task completion over both RL agents on their own and traditional sampling-based planners. In the indoor navigation task, PRM-RL successfully completes up to 215 meters long trajectories under noisy sensor conditions, and the aerial cargo delivery completes flights over 1000 meters without violating the task constraints in an environment 63 million times larger than used in training.
Simply put, "artificial intelligence” is people trying to make things do things that we’d call smart if done by people.
So what’s the big deal about that?
Well, as it turns out, a lot of people get quite wound up with the definition of "artificial intelligence.” Sometimes this is because they’re invested in a prescientific notion that machines can’t be intelligent and want to define it in a way that writes the field off before it gets started, or it’s because they’re invested in an unscientific degree into their particular theory of intelligence and want to define it in a way that constrains the field to look at only the things they care about, or because they’re actually not scientific at all and want to proscribe the field to work on the practical problems of particular interest to them.
No, I’m not bitter about having to wade through a dozen bad definitions of artificial intelligence as part of a survey. Why do you ask?
Wishful thinking won't land a man on the moon, but it might get us all killed - fortunately, though, we have people who know how to nail a good landing.
All we have to do now is preserve the fruits of their labors.
Now that a climate denier is barreling towards the presidency, other climate deniers are coming out of the woodwork, but fortunately, NASA has a great site telling the story of climate change. For those who haven’t been keeping score at home, the too-simple story is that humans have pumped vast amounts of carbon dioxide in the atmosphere in the past few decades, amounts that in the geological record resulted in disastrous temperature changes - and it’s really convenient for a lot of people to deny that.
Now, don’t worry: NASA results are in the public record, so even though Trump’s team has threatened to blind NASA’s earth sciences program and looks poised to conduct a witch hunt of climate change workers in the Department of Energy, even though climate deniers are wringing their hands in glee at the thought of a politicized EPA attacking climate science, scientists are working to save this climate data. If you want to get involved, check out climatemirror.org.
Now, I said it’s a too-simple story, and there are a lot of good references on climate change, like Henson’s The Rough Guide to Climate Change. But, technically, that could be considered a polemic, and if you want to really dig deep, you need to go for a textbook instead, one presenting a broad overview of the science without pushing an agenda. For example, Understanding Weather and Climate has a great chapter (Chapter 16 in the 4th edition) that breaks down some of the science behind global climate change (human and not) and why anthropogenic climate change is both very tricky to study - and still very worrisome.
And because I am a scientist, and I am not afraid to consider warranted arguments on both sides of any scientific question, I also want to call out Human Impacts on Weather and Climate 2/e by Cotton and Pielke, which in Chapter 8 and the Epilogue take a more skeptical view of our predictive power. In their view, well-argued in my opinion, current climate models are sensitivity studies, not forecasts; they merely establish the vulnerability of our systems to forcing factors like excess carbon, and don’t take into account areas of natural variability which might seriously alter the outcomes. And, yes, they are worried about climate groupthink.
Yes, they’re climate skeptics. But no-one is burning them at the stake. No-one is shunning them at conferences. People like me who believe in climate change read their papers with interest (especially Pielke’s work, which while it in some ways makes CO2 less of an issue and in some ways makes other human impacts seem worse). Still, Cotton and Pielke think the right approach is “sustained, stable national funding at a high level” and decry the politicization of science in either direction.
Still, do worry. Earth’s climate looks intransitive - it can get shoved from one regime to another, like the rapid-cooling Heinrich events and rapid-warming Dansgaard Oeschger events in the geological record, possibly triggered by large-scale ice sheet breakdowns and ocean circulation changes. Yes, global warming can cause global cooling by shutting down the existing pattern of global ocean circulation - and we’re pumping enough carbon dioxide into the atmosphere to simulate past triggers for such events.
Do you see why people who study climate change in enough depth to see where the science is really not settled end up walking away more unsettled about the future of our planet, not less? And why we stand up and say NO when someone else comes forward saying the “science is not settled” while acting like the science has already been settled in their favor?
"Have fun warming the planet!” Just hope it doesn’t inundate Florida. I’d love to tell you that the projected 1M sea rise discussed in the Florida resource isn’t as bad as the Geology.com map’s default 6m projections, but unfortunately, sea level seems to be rising in Florida faster than the IPCC projections, and if the science isn’t really settled, we could have a sea level rise of … jeez. After reviewing some of the research I don’t even want to tell you. The “good” news is, hey, the seas might fall too.
“Have fun rolling the dice!"
-the Centaur
SO, why's an urban fantasy author digging into the guts of Mathematica trying to reverse-engineer how Stephen Wolfram drew the diagrams of cellular automata in his book A New Kind of Science? Well, one of my favorite characters to write about is the precocious teenage weretiger Cinnamon Frost, who at first glance was a dirty little street cat until she blossomed into a mathematical genius when watered with just the right amount of motherly love. My training as a writer was in hard science fiction, so even if I'm writing about implausible fictions like teenage weretigers, I want the things that are real - like the mathematics she develops - to be right. So I'm working on a new kind of math behind the discoveries of my little fictional genius, but I'm not the youngest winner of the Hilbert Prize, so I need tools to help simulate her thought process.
And my thought process relies on visualizations, so I thought, hey, why don't I build on whatever Stephen Wolfram did in his groundbreaking tome A New Kind of Science, which is filled to its horse-choking brim with handsome diagrams of cellular automata, their rules, and the pictures generated by their evolution? After all, it only took him something like ten years to write the book ... how hard could it be?
Deconstructing the Code from A New Kind of Science, Chapter 2
Fortunately Stephen Wolfram provides at least some of the code that he used for creating the diagrams in A New Kind of Science. He's got the code available for download on the book's website, wolframscience.com, but a large subset is in the extensive endnotes for his book (which, densely printed and almost 350 pages long, could probably constitute a book in their own right). I'm going to reproduce that code here, as I assume it's short enough to fall under fair use, and for the half-dozen functions we've got here any attempt to reverse-engineer it would end up just recreating essentially the same functions with slightly different names.
Cellular automata are systems that take patterns and evolve them according to simple rules. The most basic cellular automata operate on lists of bits - strings of cells which can be "on" or "off" or alternately "live" or "dead," "true" and "false," or just "1" and "0" - and it's easiest to show off how they behave if you start with a long string of cells which are "off" with the very center cell being "on," so you can easily see how a single live cell evolves. And Wolfram's first function gives us just that, a list filled with dead cells represented by 0 with a live cell represented by 1 in its very center:
In[1]:= CenterList[n_Integer] := ReplacePart[Table[0, {n}], 1, Ceiling[n/2]]
In[2]:= CenterList[10]
Out[2]= {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}
One could imagine a cellular automata which updated each cell just based on its contents, but that would be really boring as each cell would be effectively independent. So Wolfram looks at what he calls "elementary automata" which update each cell based on their neighbors. Counting the cell itself, that's a row of three cells, and there are eight possible combinations of live and dead neighbors of three elements - and only two possible values that can be set for each new element, live or dead. Wolfram had a brain flash to list the eight possible combinations the same each way every time, so all you have are that list of eight values of "live" or "dead" - or 1's and 0's, and since a list of 1's and 0's is just a binary number, that enabled Wolfram to represent each elementary automata rule as a number:
In[3]:= ElementaryRule[num_Integer] := IntegerDigits[num, 2, 8]
In[4]:= ElementaryRule[30]
Out[4]= {0, 0, 0, 1, 1, 1, 1, 0}
Once you have that number, building code to apply the rule is easy. The input data is already a string of 1's and 0's, so Wolfram's rule for updating a list of cells basically involves shifting ("rotating") the list left and right, adding up the values of these three neighbors according to base 2 notation, and then looking up the value in the rule. Wolfram created Mathematica in part to help him research cellular automata, so the code to do this is deceptively simple…
In[5]:= CAStep[rule_List, a_List] :=
rule[[8 - (RotateLeft[a] + 2 (a + 2 RotateRight[a]))]]
... a “RotateLeft” and a “RotateRight” with some addition and multiplication to get the base 2 index into the rule. The code to apply this again and again to a list to get the history of a cellular automata over time is also simple:
In[6]:= CAEvolveList[rule_, init_List, t_Integer] :=
NestList[CAStep[rule, #] &, init, t]
Now we're ready to create the graphics for the evolution of Wolfram's "rule 30," the very simple rule which shows highly complex and irregular behavior, a discovery which Wolfram calls "the single most surprising scientific discovery [he has] ever made." Wow. Let's spin it up for a whirl and see what we get!
In[7]:= CAGraphics[history_List] :=
Graphics[Raster[1 - Reverse[history]], AspectRatio -> Automatic]
In[8]:= Show[CAGraphics[CAEvolveList[ElementaryRule[30], CenterList[103], 50]]]
Out[8]=
Uh - oh. The "Raster" code that Wolfram provides is the code to create the large images of cellular automata, not the sexy graphics that show the detailed evolution of the rules. And reading between the lines of Wolfram's end notes, he started his work in FrameMaker before Mathematica was ready to be his full publishing platform, with a complex build process producing the output - so there's no guarantee that clean simple Mathematica code even exists for some of those early diagrams.
Guess we'll have to create our own.
Visualizing Cellular Automata in the Small
The cellular automata diagrams that Wolfram uses have boxes with thin lines, rather than just a raster image with 1's and 0's represented by borderless boxes. They're particularly appealing because the lines are white between black boxes and black between white boxes, which makes the structures very easy to see. After some digging, I found that, naturally, a Mathematica function to create those box diagrams does exist, and it's called ArrayPlot, with the Mesh option set to True:
In[9]:= ArrayPlot[Table[Mod[i + j, 2], {i, 0, 3}, {j, 0, 3}], Mesh -> True]
Out[9]=
While we could just use ArrayPlot, it' s important when developing software to encapsulate our knowledge as much as possible, so we'll create a function CAGridGraphics (following the way Wolfram named his functions) that encapsulates the knowledge of turning the Mesh option to True. If later we decide there's a better representation, we can just update CAMeshGraphics, rather than hunting down every use of ArrayPlot. This function gives us this:
In[10]:= CAMeshGraphics[matrix_List] :=
ArrayPlot[matrix, Mesh -> True, ImageSize -> Large]
In[11]:= CAMeshGraphics[{CenterList[10], CenterList[10]}]
Out[11]=
Now, Wolfram has these great diagrams to help visualize cellular automata rules which show the neighbors up top and the output value at bottom, with a space between them. The GraphicsGrid does what we want here, except it by its nature resizes all the graphics to fill each available box. I'm sure there's a clever way to do this, but I don't know Mathematica well enough to find it, so I'm going to go back on what I just said earlier, break out the options on ArrayPlot, and tell the boxes to be the size I want:
In[20]:= CATransitionGraphics[rule_List] :=
GraphicsGrid[
Transpose[{Map[
ArrayPlot[{#}, Mesh -> True, ImageSize -> {20 Length[#], 20}] &, rule]}]]
That works reasonably well; here' s an example rule, where three live neighbors in a row kills the center cell :
In[21]:= CATransitionGraphics[{{1, 1, 1}, {0}}]
Out[21]=
Now we need the pattern of digits that Wolfram uses to represent his neighbor patterns. Looking at the diagrams and sfter some digging in the code, it seems like these digits are simply listed in reverse counting order - that is, for 3 cells, we count down from 2^3 - 1 to 0, represented as binary digits.
In[22]:= CANeighborPattern[num_Integer] :=
Table[IntegerDigits[i, 2, num], {i, 2^num - 1, 0, -1}]
In[23]:= CANeighborPattern[3]
Out[23]= {{1, 1, 1}, {1, 1, 0}, {1, 0, 1}, {1, 0, 0}, {0, 1, 1}, {0, 1, 0}, {0, 0,
1}, {0, 0, 0}}
Stay with me - that only gets us the first row of the CATransitionGraphics; to get the next row, we need to apply a rule to that pattern and take the center cell:
In[24]:= CARuleCenterElement[rule_List, pattern_List] :=
CAStep[rule, pattern][[Floor[Length[pattern]/2]]]
In[25]:= CARuleCenterElement[ElementaryRule[30], {0, 1, 0}]
Out[25]= 1
With all this, we can now generate the pattern of 1' s and 0' s that represent the transitions for a single rule:
In[26]:= CARulePattern[rule_List] :=
Map[{#, {CARuleCenterElement[rule, #]}} &, CANeighborPattern[3]]In[27]:= CARulePattern[ElementaryRule[30]]
Out[27]= {{{1, 1, 1}, {0}}, {{1, 1, 0}, {1}}, {{1, 0, 1}, {0}}, {{1, 0, 0}, {1}}, {{0,
1, 1}, {0}}, {{0, 1, 0}, {1}}, {{0, 0, 1}, {1}}, {{0, 0, 0}, {0}}}
Now we can turn it into graphics, putting it into another GraphicsGrid, this time with a Frame.
In[28]:= CARuleGraphics[rule_List] :=
GraphicsGrid[{Map[CATransitionGraphics[#] &, CARulePattern[rule]]},
Frame -> All]
In[29]:= CARuleGraphics[ElementaryRule[30]]
Out[29]=
At last! We' ve got the beautiful transition diagrams that Wolfram has in his book. And we want to apply it to a row with a single cell:
In[30]:= CAMeshGraphics[{CenterList[43]}]
Out[30]=
What does that look like? Well, we once again take our CAEvolveList function from before, but rather than formatting it with Raster, we format it with our CAMeshGraphics:
In[31]:= CAMeshGraphics[CAEvolveList[ElementaryRule[30], CenterList[43], 20]]
Out[31]=
And now we' ve got all the parts of the graphics which appear in the initial diagram of this page. Just to work it out a bit further, let’s write a single function to put all the graphics together, and try it out on rule 110, the rule which Wolfram discovered could effectively simulate any possible program, making it effectively a universal computer:
In[22]:= CAApplicationGraphics[rule_Integer, size_Integer] := Column[
{CAMeshGraphics[{CenterList[size]}],
CARuleGraphics[ElementaryRule[rule]],
CAMeshGraphics[
CAEvolveList[ElementaryRule[rule], CenterList[size],
Floor[size/2] - 1]]},
Center]In[23]:= CAApplicationGraphics[110, 43]
Out[23]=
It doesn' t come out quite the way it did in Photoshop, but we' re getting close. Further learning of the rules of Mathematica graphics will probably help me, but that's neither here nor there. We've got a set of tools for displaying diagrams, which we can craft into what we need.
Which happens to be a non-standard number system unfolding itself into hyperbolic space, God help me.
Wish me luck.
-the Centaur
P.S. While I' m going to do a standard blogpost on this, I' m also going to try creating a Mathematica Computable Document Format (.cdf) for your perusal. Wish me luck again - it's my first one of these things.
P.P.S. I think it' s worthwhile to point out that while the tools I just built help visualize the application of a rule in the small …
In[24]:= CAApplicationGraphics[105, 53]
Out[24]=
... the tools Wolfram built help visualize rules in the very, very large:
In[25]:= Show[CAGraphics[CAEvolveList[ElementaryRule[105], CenterList[10003], 5000]]]
Out[25]=
That's 10,000 times bigger - 100 times bigger in each direction - and Mathematica executes and displays it flawlessly.
I think I'll be posting this everywhere for a while … LIQUID FIRE, my third novel, is now available for preorder on Amazon. I talk a bit more about this on the Dakota Frost blog, but after a lot of work with beta readers, editing, and my editor, I'm very proud of this book, which takes Dakota out of her comfort zone in Atlanta and brings her to the San Francisco Bay, where she encounters romance, danger, magic, science, art, mathematics, vampires, werewolves, and the fae. It comes out May 22, but you can preorder it now on Amazon! Go get it! You'll have a blast.
And, almost at the same time, I found out this is coming out on May 22 as well…
TWELVE HOURS LATER is also available for preorder on Amazon Kindle and CreateSpace. Put together by the Treehouse Writers, TWELVE HOURS LATER is a collection of 24 steampunk stories, one for every hour in the day - many of them in linked pairs, half a day apart … hence "Twelve Hours Later". My two stories in the anthology, "The Hour of the Wolf" and "The Time of Ghosts", feature Jeremiah Willstone, the protagonist of "Steampunk Fairy Chick" in the UnCONventional anthology … and also the protagonist of the forthcoming novel THE CLOCKWORK TIME MACHINE from Bell Bridge Books. (It's also set in the same universe as "The Doorway to Extra Time" from the anthology of the almost identical name).
And, believe it or not, I may have something else coming out soon … stay tuned. :-)
-the Centaur
I've felt quite harried over the past few weeks … and talking with another author, I realized why.
In April, I finally finished my part of Dakota Frost #3, LIQUID FIRE - sending comments to the publisher Bell Bridge Books on the galley proofs, reviewing cover ideas, contributing to the back cover copy, writing blogposts. I also as part of Camp Nanowrimo finished a rough rough draft of Dakota Frost #4, SPECTRAL IRON. But at the same time, I had recently finished a short story, "Vogler's Garden", and have been sending it out to quite a few places.
In May, we expect LIQUID FIRE will be out, I have two stories in the anthology TWELVE HOURS LATER, and I have three guest blog posts coming out, one on "Science is Story: Science, Magic, and the Thin Line Between" on the National Novel Writing Month blog which has gotten some traction. And I'll be speaking at the Clockwork Alchemy conference. Oh, and I'm about to start responding to Bell Bridge's feedback on my fourth novel, THE CLOCKWORK TIME MACHINE.
Holy cow. No wonder I feel so harried! But it's all for a good cause.
-the Centaur
Pictured: a friend at work shattered his monitor and inadvertently made art.
Once again, I will be giving a talk on The Science of Airships at Clockwork Alchemy this year, this time at 11AM on Monday. I had to suffer doing all the airship research for THE CLOCKWORK TIME MACHINE, so you should too! Seriously, I hope the panel is fun and informative and it was received well at previous presentations. From the online description:
Steampunk isn't just brown, boots and buttons: our adventurers need glorious flying machines! This panel will unpack the science of lift, the innovations of Count Zeppelin, how airships went down in flames, and how we might still have cruise liners of the air if things had gone a bit differently. Anthony Francis is a science fiction author best known for his Dakota Frost urban fantasy series, beginning with the award winning FROST MOON. His forays into Steampunk include two stories and the forthcoming novel THE CLOCKWORK TIME MACHINE.
Yes, yes, I know THE CLOCKWORK TIME MACHINE is long in forthcoming, but at least it's closer now. I'll also be appearing on two panels, "Facts with Your Fiction" moderated by Sharon Cathcartat 5pm on Saturday and "Multi-cultural Influences in Steampunk" moderated by Madeline Holly at 5pm on Sunday. With that, BayCon and Fanime, looks to be a busy weekend.
-the Centaur