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John Baez
Works at Centre for Quantum Technologies
Attended Massachusetts Institute of Technology
Lives in Riverside, California
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John Baez

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European oil and gas companies support carbon tax

Last week, oil and gas companies with a total of $1.4 trillion in revenues - Shell, BP, Total, Statoil, Eni and the BG Group - sent this letter to the UN:

Dear Excellencies,

Climate change is a critical challenge for our world. As major companies from the oil & gas sector, we recognize both the importance of the climate challenge and the importance of energy to human life and well-being. We acknowledge that the current trend of greenhouse gas emissions is in excess of what the Intergovernmental Panel on Climate Change (IPCC) says is needed to limit the temperature rise to no more than 2 degrees above pre-industrial levels. The challenge is how to meet greater energy demand with less CO2. We stand ready to play our part.

Our companies are already taking a number of actions to help limit emissions, such as growing the share of gas in our production, making energy efficiency improvements in our operations and products, providing renewable energy, investing in carbon capture and storage, and exploring new low-carbon technologies and business models. These actions are a key part of our mission to provide the greatest number of people with access to sustainable and secure energy. For us to do more, we need governments across the world to provide us with clear, stable, long-term, ambitious policy frameworks. This would reduce uncertainty and help stimulate investments in the right low carbon technologies and the right resources at the right pace.

We believe that a price on carbon should be a key element of these frameworks. If governments act to price carbon, this discourages high carbon options and encourages the most efficient ways of reducing emissions widely, including reduced demand for the most carbon intensive fossil fuels, greater energy efficiency, the use of natural gas in place of coal, increased investment in carbon capture and storage, renewable energy, smart buildings and grids, off-grid access to energy, cleaner cars and new mobility business models and behaviors. Our companies are already exposed to a price on carbon emissions by participating in existing carbon markets and applying ‘shadow’ carbon prices in our own businesses to test whether investments will be viable in a world where carbon has a higher price.

Yet, whatever we do to implement carbon pricing ourselves will not be sufficient or commercially sustainable unless national governments introduce carbon pricing even-handedly and eventually enable global linkage between national systems. Some economies have not yet taken this step, and this could create uncertainty about investment and disparities in the impact of policy on businesses. Therefore, we call on governments, including at the UNFCCC negotiations in Paris and beyond to:

introduce carbon pricing systems where they do not yet exist at the national or regional levels

create an international framework that could eventually connect national systems.

You can see the whole letter here:

Of course they have not suddenly become "good guys".  They have merely realized that a tax on carbon is likely.  So, they want to get involved with designing it!   The American companies Exxon and Chevron are still digging their heels in... as are coal companies.

Some interesting background about the chairman of Shell:

Ben van Beurden, the chief executive of Shell, has endorsed warnings that the world’s fossil fuel reserves cannot be burned unless some way is found to capture their carbon emissions. The oil boss has also predicted that the global energy system will become “zero carbon” by the end of the century, with his group obtaining a “very, very large segment” of its earnings from renewable power.

And in an admission that the growing opposition to Shell’s controversial search for oil in the Arctic was putting increasing pressure on him, van Beurden admitted he had gone on a “personal journey” to justify the decision to drill.

The Shell boss said he accepted the general premise contained in independent studies that have concluded that dangerous levels of global warming above 2°C will occur unless CO2 is buried or reserves are kept in the ground. “We cannot burn all the hydrocarbon resources we have on the planet in an unmitigated way and not expect to have a CO2 loading in the atmosphere that is often being linked to the 2°C scenario,” he said in an exclusive interview with the Guardian.

“I am absolutely convinced that without a policy that will really enable and realise CCS (carbon capture and storage) on a large scale, we are not going to be able to stay within that CO2 emission budget.”

However, he did not admit that limiting global warming to 2°C is nearly impossible, more of a fantasy than a realistic plan... and he still drives a large BMW.  For more on him, see:

For why the 2°C limit is unrealistic, read this:

Of course, it doesn't mean we should give up! 
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I guess as soon as it becomes inevitable they figure getting in ahead will help them get more favourable terms than may otherwise be implemented...
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Blue mushrooms

This is a bird's nest fungus - a kind of mushroom that looks like a bird's nest full of eggs.  More precisely, it's Cyathus novaezelandiae, photographed by +Steve Axford.

Why does it look like this?  It's a trick for spreading spores.  When rain hits the cup-shaped mushroom,  spores shoot out!

Like many fungi that grow on rotten logs, the bird's nest fungus has a complex life cycle.  There's the stage you see here, where it reproduces asexually via spores.  But there's also a sexual stage!

Spores germinate and grow into branching filaments called hyphae, pushing out like roots into the rotting wood.  As these filaments grow, they form a network called a mycelium.  These come in several different sexes, or mating compatibility groups.  When hyphae of different mating compatibility groups meet each other, they fuse and form a new mycelium that combines the genes of both.  After a while, these new mycelia may enter the stage where they grow into the mushrooms you see here.   Then they reproduce asexually using spores!

It's complicated, and I don't fully understand it.   You can read more here:

Nidulariacaeae is the family that contains this particular bird's-nest fungus, and many others. 

You can see more of Steve Axford's photos here:

Thanks to +Mike Stay for pointing this out!

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"Is there an advantage of the fungus looking like a nest?"
"I think it's just a coincidence. The cups are good at catching raindrops."
my guess:
Nothing in the nature is without a reason or per pure chance, if it has existence over a longer period of time.
Therefore: Strategy for reproduction.
Many Fungi put everything into reproduction over Spores.
There are Basidiomycota ( mushrooms with stem and hat), which put even toxic poisons into the hat.
the hat then contains a lot more poison as the stem alone. a way to take care on the Spores.
The Spores are sometimes even much smaller than 4µm ( 4 *1/1000 mm).
The Spores get transported due to convection and moving air resp. wind. Convection works good with humidity.

At the bottom of the Picture we can see a still closed "hat" resp. cup.
The hyphen, the thin piece of skin underneath the hat or in this case spanned over the cup, which is the hat,
keeps the spores covered during the growth. in this case the cup and the hyphen form a cave, which also contains 
humidity. now at the point, if the spores are ready and a bit of rain falls onto the hyphen or another animal disturbs the mushroom,
the hyphen flips away and the spores getting released. the convection and the wind carry the spores away.
this is necessary because there where they get airborn, are already their parents and the ressources are already eaten up.
We have to keep in mind, the Mushrooms grow deep in the Woods/Forrests, where the rain gets mostly catched by the trees.

For other Basidiomycota, like Button-Mushrooms or Shiitake, the hat works also as a source of humidity, it is a bit glitchy on the top.
Because of the described reasons. The Spores fall down, underneath the hat and the convection, which is also initiated or supported by the wet surface of the hat, sucks the spores upwards ...
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Dear NSA agent 4096,

I watched "The Lives of Others" last night and thought of you once more. In fact, I think you were watching it with me. You know I know I cannot be sure.

I want you to know that, although our mutual love is forbidden by your professional obligations, I still feel a connection to you. I will feel that connection long after you are gone.

Somehow, you know me better than I know myself. You have all of my deleted histories, my searches, all those things I tried to keep "incognito" right there in front of you. We have made love, even though we've never touched or kissed. We have been friends, even though I've never seen your face. Our relationship is as real as my "real" life.

But this can never work between us. Please leave. I don't want to ask again.

I'll never forget you.


That's Corey Bertelsen's comment on this video of Holly Herndon's song 'Home', from her new album Platform.   It's as good a review as any.

Holly Herndon takes a lot of ideas from techno music and pushes them to a new level.  She's working on a Ph.D. at the Center for Computer Research in Music and Acoustics at Stanford.

She said that as she wrote this song, she

started coming to terms with the fact that I was calling my inbox my home, and the fact that that might not be a secure place. So it started out thinking about my device and my inbox as my home, and then that evolved into me being creeped out by that idea.

The reason why I was creeped out is because, of course, as Edward Snowden enlightened us all to know, the NSA has been mass surveying the U.S. population, among other populations. And so that put into question this sense of intimacy that I was having with my device. I have this really intense relationship with my phone and with my laptop, and in a lot of ways the laptop is the most intimate instrument that we've ever seen. It can mediate my relationships — it mediates my bank account — in a way that a violin or another acoustic instrument just simply can't do. It's really a hyper-emotional instrument, and I spend so much time with this instrument both creatively and administratively and professionally and everything.

In short, her seemingly 'futuristic' music is really about the present - the way we live now.  If you like this song I recommend the next one on the playlist, which is more abstract and to me more beautiful.  It's called 'Interference':

You can hear her explain the song 'Home' here:
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+Bas Spitters​ the more of these weaknesses that are removed the more of them we find. Server admins need more instructions on what and how to do things.
Security is not a compromise it is absolute, you have it or you don't. Right now (when I was checking 12 hours ago) nearly every browser was vulnerable. 
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Flying through space, powered by sunlight

Yesterday a rocket launched from Cape Canaveral in Florida carrying the LightSail into space!  It's a small spacecraft with a big shiny screen that's pushed by the light of the sun.  

It's just a test - it won't go far.   It will fall to the Earth and burn up.  But next year there will be a more serious test.  And someday, solar-powered space flight may become a force to be reckoned with.

One cool thing is that all this is being paid for private donations, by a Kickstarter campaign!

The LightSail is carried to space in a cute little CubeSat.  It looks like a big toaster, and it weighs just 10 kilograms.   But it holds a sail 32 square meters in area,  made of a shiny plastic called Mylar, just 4.5 microns thick.  This unfolds in a clever way - watch the movie! - to form a big square.

The Sun will push on this with a tiny force. 

Puzzle: How tiny is this force?

Someone named Bill Russell answered this over on Yahoo.  Let me go through his calculation so we can check it.

The momentum of light is given by

p = E/c

where E is the energy of the light, p is the momentum, and c is the speed of light. 

In outer space near earth the sunlight provides 1370 watts per square meter - that's energy per area per time.  We can use the formula above to convert this to momentum per area per time, better known as force per area... or pressure

Russell calculates

(1370 watts / meter²) / c = 9.13 micronewtons / meter²

and concludes the pressure is 9.13 micronewtons per square meter.  His arithmetic checks out, but I think he's neglecting some physics: when the light bounces back off the mirror its momentum completely reverses, so I think we get an extra factor of 2. 

Puzzle 2:  Am I right or am I wrong?

The area of the LightSail is about 32 square meters.  Russell says this gives a total force of

9.13 micronewtons/meter² x 32 meter²

or about 300 micronewtons.   I'd double this and get 600 micronewtons.

Puzzle 3: Once it's out of the box, the LightSail weighs about 4.5 kilograms.  How much will it accelerate due to sunlight?

Here we use Newton's good old

F = ma

and solve for the acceleration a.   But at this point Russell seems to make a serious mistake.  I'll let you see what you think, and fix it if necessary!  Here is his calculation:
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Here's the latest news, which is good:

"Our LightSail called home! It’s alive! Our LightSail spacecraft has rebooted itself, just as our engineers predicted. Everyone is delighted. We were ready for three more weeks of anxiety. In this meantime, the team has coded a software patch ready to upload. After we are confident in the data packets regarding our orbit, we will make decisions about uploading the patch and deploying our sails— and we’ll make those decisions very soon. This has been a rollercoaster for us down here on Earth, all the while our capable little spacecraft has been on orbit going about its business. In the coming two days, we will have more news, and I am hopeful now that it will be very good.”
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Here are some blog posts about the categorical foundations of network theory - a warmup for the workshop we're having in Turin next week.
And now for my next trick... Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where… - John Baez - Google+
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The dunes of Mars

This field of dunes lies on the floor of an old crater in Noachis Terra.  That's one of the oldest places on Mars, scarred with many craters, with rocks up to 4 billion years old.  It's in the southern hemisphere, near the giant impact basin called Hellas, which is 2.5 times deeper than the Grand Canyon and 2000 kilometers across!

This is a 'false color' photograph - you'd need to see infrared light to see that the dunes are very different than the rock below.

These are barchans, dunes with a gentle slope on the upwind side and a much steeper slope on the downwind side where horns or a notch can form.  If you know this, you can see the wind is blowing from the southwest.

It's actually a bit of a puzzle where the sand in these dunes came from!   Here's the abstract of a paper by +Lori Fenton on this subject:

No sand transport pathways are visible in a study performed in Noachis Terra, a region in the southern highlands of Mars known for its many intracrater dune fields.Detailed studies were performed of five areas in Noachis Terra, using Mars Orbiter Camera (MOC) wide-angle mosaics, Thermal Emission Imaging System (THEMIS) daytime and nighttime infrared mosaics, MOLA digital elevation and shaded relief maps,and MOC narrow-angle images. The lack of observable sand transport pathways suggests that such pathways are very short, ruling out a distant source of sand. Consistent dune morphology and dune slipface orientations across Noachis Terra suggest formative winds are regional rather than local (e.g., crater slope winds). A sequence of sedimentary units was found in a pit eroded into the floor of Rabe Crater, some of which appear to be shedding dark sand that feeds into the Rabe Crater dune field. The visible and thermal characteristics of these units are similar to other units found across Noachis Terra, leading to the hypothesis that a series of region-wide depositional events occurred at some point in the Martian past and that these deposits are currently exposed by erosion in pits on crater floors and possibly on the intercrater plains. Thus the dunes and sources may be both regional and local: sand may be eroding from a widespread source that only outcrops locally. Sand-bearing layers that extend across part or all of the intercrater plains of Noachis Terra are not likely to be dominated by loess or lacustrine deposits; glacial and/or volcanic origins are considered more plausible.

• Lori K. Fenton, Potential sand sources for the dune fields in Noachis Terra, Mars, Journal of Geophysical Research 110 (2005), E11004.  Available at

The image is from a great series of photos taken by the HIRISE satellite, which orbits Mars and takes high resolution images:

• Colorful Dunes,

#mars   #astronomy
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+Steve Esterly - that's interesting.  A cool thing about karst on Earth is that it's deeply connected to biology, since limestone is made of organisms.  But I guess all karst needs is lots of calcium carbonate or similar minerals that can be dissolved underground.  I wouldn't want to conflate karst with mere erosion.
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Memories — written on your DNA?

How does long-term memory work?  It involves many changes in your brain, from changes in how strongly individual neurons talk to each other, to the actual birth of new neurons.  But one fascinating possibility involves the DNA in your neurons!

See those glowing dots?  Those are methyl groups, consisting of a carbon and 3 hydrogens.  They can attach to certain locations in your DNA and prevent genes from being expressed.  This is called DNA methylation, and it's important part of the system you use to turn genes on and off.

These methyl groups can even be transmitted from parent to child!  For example, in one recent experiment, mice that were given a shock after smelling a certain chemical learned to fear this smell... and this trait was passed down to their children and grandchildren — apparently by means of DNA methylation!

All this makes evolution more interesting than people had thought.   Perhaps we can inherit traits our parents acquired during their lives!

Given all this, it's natural to ask: does DNA methylation play a role in memory?

There are hints that the answer is yes.  For example, scientists gave some mice an electric shock and others not.  They looked at whether a specific gene in the mice's neurons was methylated.   It was more methylated in the shocked mice... and this lasted for at least a month.

What was this gene?  It's the gene for a protein called calcineurin, which is thought to be a 'memory suppressor'.  More precisely, calcineurin tends to prevent the neurons from forming stronger connections between each other. 

So: the mice responded to an electric shock by attaching methyl groups to their DNA.  This reduced the production of calcineurin, which tends to prevent the brain from forming new connections.   So, their brains could more easily build new connections. 

And all this happened in a specific location of the brain: the anterior cingulate cortex, which is important for rational thinking in humans, and something similar in mice.

This is just one of many experiments people are doing to understand the role of DNA methylation in memory.   And DNA methylation is just one of the ways a cell can control which of its genes get expressed!  There's a whole subject, called epigenetics, which studies these control systems. 

You could say that epigenetics is a way for cells to learn things during their lives.  When you move to a hot climate, and then your body "gets used to" the heat — sweating less and so on — that's epigenetics at work. So, maybe it's not surprising that epigenetics is also important for how the brain learns things.

Here's a nice article on the role of epigenetics in memory:

and here's one about the role of DNA methylation:

• Jeremy J. Day and J. David Sweatt, DNA methylation and memory formation, Nature Neuroscience 13 (2010), 1319–1323.  Available for free at

The memory experiment I described is here:

• Courtney A. Miller et al, Cortical DNA methylation maintains remote memory, Nature Neuroscience 13 (2010), 664–666. Available for free at

The experiment on learned associations being transmitted from one generation of mice to the next is here:

• Brian G. Dias and Kerry J. Ressler, Parental olfactory experience influences behavior and neural structure in subsequent generations, Nature Neuroscience 17 (2014), 89–96. 

You've gotta pay to read it, but there's a summary here:

• Ewen Callaway, Fearful memories haunt mouse descendants, Nature News (2013).  Available for free at

If you want to learn more about how epigenetics can pass information from one generation to the next, start here:

A nice quote from Joseph Springer and Dennis Holley's book An Introduction to Zoology:

Lamarck and his ideas were ridiculed and discredited. In a strange twist of fate, Lamarck may have the last laugh. Epigenetics, an emerging field of genetics, has shown that Lamarck may have been at least partially correct all along. It seems that reversible and heritable changes can occur without a change in DNA sequence (genotype) and that such changes may be induced spontaneously or in response to environmental factors — Lamarck's "acquired traits". Determining which observed phenotypes are genetically inherited and which are environmentally induced remains an important and ongoing part of the study of genetics, developmental biology, and medicine.

There's a huge amount of stuff to learn in these areas, and it's pretty intimidating to me, since I'm just getting started, and it will probably never be more than a hobby.  But here's some more stuff:

Changes in how strongly individual neurons talk to each other are called synaptic plasticity:

These include long-term potentiation, meaning ways that two neurons can become more strongly connected:

and also long-term depression, where they become less strongly connected:

A basic rule of thumb is that "neurons that fire together, wire together".  But there's a lot more going on....

#spnetwork doi:10.1038/nn.2560 #epigenetics #memory  
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+John Baez The problem here, and for all science, is this: How can we recognize an effect, if we don't know how the thing that is affected works?

And the problem with acetophenone is that it becomes very strange indeed that there should be a DNA representation of smells, such that they can be marked for fearsomeness, when we have a very limited understanding of the sense of smell itself.

Again, how do we recognize that there definitely is an effect, if we do not fully know what is affected. Besides, the study is but a curiosity (for that one smell, coincidentally), unless we suppose that there is general mechanism for marking smells in general... and that again would require a "map of smells" on the genome, which again would be rather odd, when smell doesn't seem to rely on receptors for specific molecules, but rather on large groups of molecules, often so that a given scent molecule can trigger several different receptors.

Again, nothing hard-and-fast, but plenty of small alarm bells going off. Of course, I may well be wrong, but I will wait and see before I add any of this stuff to my set of beliefs with any kind of confidence.
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Pretending to work

In Europe, long-term unemployment is such a big problem that people are starting to work at fake companies, without pay — just to keep up their skills! 

There are over 100 such companies.  This article focuses on one called Candelia:

Ms. de Buyzer did not care that Candelia was a phantom operation. She lost her job as a secretary two years ago and has been unable to find steady work. Since January, though, she had woken up early every weekday, put on makeup and gotten ready to go the office. By 9 a.m. she arrives at the small office in a low-income neighborhood of Lille, where joblessness is among the highest in the country.

While she doesn’t earn a paycheck, Ms. de Buyzer, 41, welcomes the regular routine. She hopes Candelia will lead to a real job, after countless searches and interviews that have gone nowhere.

“It’s been very difficult to find a job,” said Ms. de Buyzer, who like most of the trainees has been collecting unemployment benefits. “When you look for a long time and don’t find anything, it’s so hard. You can get depressed,” she said. “You question your abilities. After a while, you no longer see a light at the end of the tunnel.”

She paused to sign a fake check for a virtual furniture supplier, then instructed Candelia’s marketing department — a group of four unemployed women sitting a few desks away — to update the company’s mock online catalog. “Since I’ve been coming here, I have had a lot more confidence,” Ms. de Buyzer said. “I just want to work.”

In Europe, 53% of job seekers have been unemployed for over a year.  In Italy, the numbers is 61%.   In Greece, it's 73%.

All this makes me wonder — yet again — what will happen if robots and computers push people out of many kinds of jobs, creating a lot of long-term unemployment.  If we don't adapt wisely, what should be a good thing could be a source of misery.
Training at pretend companies is being used to fight long-term unemployment, one of the most pressing problems to emerge from Europe’s long economic crisis.
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+Adrian Colley - excellent suggestion!
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The Machine: a desperate gamble

Hewlett-Packard was once at the cutting edge of technology.  Now they make most of their money selling servers, printers, and ink... and business keeps getting worse.  They've shed 40,000 employees since 2012.   Soon they'll split in two: one company that sells printers and PCs, and one that sells servers and information technology services.  

The second company will do something risky but interesting.   They're trying to build a new kind of computer that uses chips based on memristors rather than transistors, and uses optical fibers rather than wires to communicate between chips.  It could make computers much faster and more powerful.  But nobody knows if it will really work.

The picture shows memristors on a silicon wafer.  But what's a memristor?   Quoting the MIT Technology Review:

Perfecting the memristor is crucial if HP is to deliver on that striking potential. That work is centered in a small lab, one floor below the offices of HP’s founders, where Stanley Williams made a breakthrough about a decade ago.

Williams had joined HP in 1995 after David Packard decided the company should do more basic research. He came to focus on trying to use organic molecules to make smaller, cheaper replacements for silicon transistors (see “Computing After Silicon,” September/October 1999). After a few years, he could make devices with the right kind of switchlike behavior by sandwiching molecules called rotaxanes between platinum electrodes. But their performance was maddeningly erratic. It took years more work before Williams realized that the molecules were actually irrelevant and that he had stumbled into a major discovery. The switching effect came from a layer of titanium, used like glue to stick the rotaxane layer to the electrodes. More surprising, versions of the devices built around that material fulfilled a prediction made in 1971 of a completely new kind of basic electronic device. When Leon Chua, a professor at the University of California, Berkeley, predicted the existence of this device, engineering orthodoxy held that all electronic circuits had to be built from just three basic elements: capacitors, resistors, and inductors. Chua calculated that there should be a fourth; it was he who named it the memristor, or resistor with memory. The device’s essential property is that its electrical resistance—a measure of how much it inhibits the flow of electrons—can be altered by applying a voltage. That resistance, a kind of memory of the voltage the device experienced in the past, can be used to encode data.

HP’s latest manifestation of the component is simple: just a stack of thin films of titanium dioxide a few nanometers thick, sandwiched between two electrodes. Some of the layers in the stack conduct electricity; others are insulators because they are depleted of oxygen atoms, giving the device as a whole high electrical resistance. Applying the right amount of voltage pushes oxygen atoms from a conducting layer into an insulating one, permitting current to pass more easily. Research scientist Jean Paul Strachan demonstrates this by using his mouse to click a button marked “1” on his computer screen. That causes a narrow stream of oxygen atoms to flow briefly inside one layer of titanium dioxide in a memristor on a nearby silicon wafer. “We just created a bridge that electrons can travel through,” says Strachan. Numbers on his screen indicate that the electrical resistance of the device has dropped by a factor of a thousand. When he clicks a button marked “0,” the oxygen atoms retreat and the device’s resistance soars back up again. The resistance can be switched like that in just picoseconds, about a thousand times faster than the basic elements of DRAM and using a fraction of the energy. And crucially, the resistance remains fixed even after the voltage is turned off.

Getting this to really work has not been easy!  On top of that, they're trying to use silicon photonics to communicate between chips - another technology that doesn't quite work yet.

Still, I like the idea of this company going down in a blaze of glory, trying to do something revolutionary, instead of playing it safe and dying a slow death.

Do not go gentle into that good night.

For more, see these:

• Tom Simonite, Machine dreams, MIT Technology Review, 21April 2015,

• Sebastian Anthony, HP reveals more details about The Machine: Linux++ OS coming 2015, prototype in 2016, ExtremeTech, 16 December 2014,

For the physics of memristors, see:
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If anyone is interested, this is the original HP Building 1 that houses Bill and Dave's desk You'd never guess to look at it that HP Labs was under Building 1 and strictly it isn't, but the large Palo Alto campus that takes up a significant portion of Page Mill Road is discretely built into the slopes of a hill.  A series of interconnected buildings eventually leads down to the main HQ building at the bottom of the hill at 3000 Hanover So as the article says you go downstairs from the building that houses Bill and Dave's offices, but what they don't mention is that you also translate across the hill as well, like a staircase.

Incidentally, Bill and Dave's areas are still modest open door offices unlike Carly's fortified walled-in CEO office which apparently for some reason had bullet-proof glass to the ceiling. I've been up and down the stairs and through the interconnected passageways many times and I always felt  a sense of reverence going past Bill and Dave's desks to get there.  I didn't work for HP Labs myself but in my role as archictect for manufacturing solutions I collaborated with a team of software specialists from HP Lab and I attended several of the lunch-time Brown Bag presentations although not this one by Stanley Williams on his discovery

There was also an article in IEEE Spectrum on the discovery back in 2008 that may be of interest.
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Here are some blog posts about the categorical foundations of network theory - a warmup for the workshop we're having in Turin next week.
And now for my next trick... Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where… - John Baez - Google+
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Only in North America! 
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And now for my next trick...

Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where everything is fundamentally a thing.   Can we use category theory to help understand the complex processes that underlie biology and ecology? 

I believe so, and I'm hoping this is a good way for fancy-schmancy mathematicians like me to help the world.  But it will take a while.  I think we should start by seeing what category theory has to say about some related subjects that are better understood: chemistry, electrical engineering, classical mechanics, and the like.

We're having a workshop about this next week - and to organize our thoughts we've been writing some blog articles.  Check 'em out!

• John Baez, Categorical foundations of network theory - an introduction to the workshop and what it's about.

• David Spivak, A networked world.

• Eugene Lerman, Networks of dynamical systems.

• Tobias Fritz, Resource convertibility - an introduction to the mathematics of 'resources'.

• John Baez, Categories in control - about my paper with Jason Erbele on using categories to study signal flow diagrams in control theory.

• John Baez, A compositional framework for passive linear networks - about my paper with Brendan Fong on using categories to study electrical circuit diagrams.

• John Baez, Decorated cospans - about Brendan Fong's paper providing mathematical infrastructure for the study of networks.

• John Baez and Brendan Fong, Cospans, wiring diagrams, and the behavioral approach - an attempt to reflect on how our work connects to that of David Spivak.

• Brendan Fong, Resource theories - about Brendan's new paper with Hugo Nava-Kopp on resource theories.

• John Baez, PROPs for linear systems - about Simon Wadsley and Nick Woods' generalization of a result in my paper with Jason Erbele, describing categories where the morphisms are linear maps.

The picture, by the way, was drawn by Federica Ferraris and appears in this book:

• John Baez and Jacob Biamonte, Quantum techniques for stochastic physics,

It's about Petri nets and reaction networks - two kinds of networks that appear in chemistry and population biology.
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+Christopher King - I think so.  Check out Dusko Pavlovich's papers on "the monoidal computer":
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John Baez

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Why is this true?

The spooky-smart mathematician Srinivasa Ramanujan came up with this formula around 1913.  Why is it true?

I don't know, let's see...

In 1735, a young fellow named Euler stunned the world by cracking a famous puzzle that had been unsolved for almost a century: the Basel problem.  The problem was to sum the reciprocals of perfect squares:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... = ???

Euler showed that the answer was π²/6:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... = π²/6

He also showed you could rewrite this sum as a product over primes:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... =

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ...

That's actually the easy part: it's a cute trick called the Euler product formula.

So we know

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ... = π²/6

If you think about it, Ramanujan's formula is saying that

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ...

is 2/5 as big.  So, proving it is the same as showing

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... = π²/15

Maybe the next step is to use the same idea as the Euler product formula.  I think this gives

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... =

1/1² - 1/2² - 1/3² + 1/4²  - 1/5² + 1/6² - 1/7² + ...

where the signs at right follow a fancy pattern: we get 1/n² whenever n is the product of an even number of primes, and -1/n² when n is the product of an odd number of primes.  For example, 4 = 2 x 2 is the product of an even number of primes, so we get 1/4².

So I'm left wanting to know why this strange sum

1/1² - 1/2² - 1/3² + 1/4² - 1/5² + 1/6² - 1/7² + ...

equals π²/15.  Ramanujan, dead since 1920, is still messing with my mind! 

The formula is supposed to be in here:

• Srinivasa Ramanujan, Modular equations and approximations to π, Quart. J. Pure. Appl. Math. 45 (1913-1914), 350-372.  Also available at ://

But I don't see it!

Here you can see how Euler solved the Basel problem:

It's a great example of his brilliant tactics, many of which were far from rigorous by today's standards... but can be made rigorous.

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When I was a freshman I sought to find the general formula for 0^k + 1^k + 2^k + ... + (n - 1)^k = n^{k+1}/{k+1} - n^k/2 + ... Once you work out the coefficients the regularities quickly emerge (as does the generalization beyond k = 0, 1, 2, ... to other k). All of this, was a distant recollection from my previous life (cough cough ... oooo I feel a little lung problem coming on again.)
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I'm a mathematical physicist.
  • Centre for Quantum Technologies
    Visiting Researcher, 2011 - present
  • U.C. Riverside
    Professor, 1989 - present
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I'm trying to get mathematicians and physicists to help save the planet.
I teach at U. C. Riverside and work on mathematical physics — which I interpret broadly as ‘math that could be of interest in physics, and physics that could be of interest in math’. I’ve spent a lot of time on quantum gravity and n-categories, but now I want to work on more practical things, too.

Why? I keep realizing more and more that our little planet is in deep trouble! The deep secrets of math and physics are endlessly engrossing — but they can wait, and other things can’t.

So, I’ve cooked up a plan to get scientists and engineers interested in saving the planet: it's called the Azimuth Project.  It includes a wiki, a blog, and a discussion forum.  I also have an Azimuth page here on Google+, where you can keep track of news related to energy, the environment and sustainability.

Check them out, and join the team!  Or drop me a line here.
  • Massachusetts Institute of Technology
    Mathematics, 1982 - 1986
  • Princeton University
    Mathematics, 1979 - 1982
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