magic at night

We are currently in Tromsø, Norway, for the turn of the calendar year. The sun does not rise but at night one can see a special light show: Northern Lights.



This image was taken with 15sec exposure (no post-processing); but it looks different from what the human eye sees - a fainter picture but with more structure which actually moves and changes.
In order to see it we had to drive away from city lights and in order to get to clear enough sky we actually had to drive to Finland, which took about 2 1/2 hours. The temperature dropped from -2C in Tromsø to about -26C inland and I find this steep decline quite amazing.


added later: I wish everybody a Happy New Year and good luck in 2015 - we may need it.

2015

Next year will be interesting for several reasons:

The LHC will start up again at higher energies and perhaps show us some physics beyond the standard model.

Advanced LIGO should perform the first observing run and this time chances are good that it will actually detect gravitational waves.

We should see Pluto and Charon at close distance for the first time ever.

The FOMC will probably decide to raise interest rates.

The long awaited tv series Better Call Saul will start with its premier episode in February.
I admit that the latter was actually the reason for writing this blog post ...

MONIAC



"The MONIAC — short for Monetary National Income Analogue Computer — was a machine that analyzed economic data using, yes, hydraulics. Basically, it pumped water through pipes and tanks in an effort to simulate an economy and make predictions about its future. [..]
The machine’s various tanks and flows represent different parts of an economy, such as banks, consumer spending, personal savings, taxes, foreign holdings, and more. As McRobie explains, if you find that the personal savings tank is getting too full and you want to encourage more investment, you can simulate a drop in interest rates by widening the bank’s valve so that money flows more freely through the system."
Wired

I guess MONIAC is the wet dream of every Keynesian central planner; I suspect Mr. Abe is using his right now to figure out where all that Yen-water went that he printed. Perhaps he should have closed the carry trade valve to avoid recession?

Artiste and vectors

I just read Henning Dekant's blog post contemplating an alternative history with William K. Clifford enjoying a longer life and more influence on physics. It introduces us to 'geometric algebra' with the central idea to define the non-commutative product of two vectors as
AB = A*B + A/\B
where * is the usual scalar product and /\ the anti-commutative wedge product.

In a conventional textbook this is a big no-no, because it adds a scalar to a vector, but it nicely relates to complex numbers in 2D and quaternions in 3D and it supposedly simplifies everything in 2D and a lot in 3D.
I added this to my to-do list of things I need to understand better, which already contains an entry about algebraic topology and another about non-commutative geometry (more about that perhaps later).

Btw it seems that Henning Dekant and Robert R. Tucci have (re)created Artiste as a company to develop software and software patents for quantum computers. Of course, the necessary hardware does not really exist yet, but perhaps it is not such a bad idea to try this time to think about software before quantum computers become available. (Is 'hardware' really a good term for a quantum computer?)
How would classical computers look like if e.g. Python would have been developed already in the 1940s? Or in a less distant alternative universe - how would computers look like if a Lisp interpreter had been implemented before the first Fortran compiler?

Interstellar - less than stellar (spoilers!)

I am pretty sure that an astronaut who falls into a black hole would not end up behind the bookshelf of his daughter - even if it turns out that the bookshelf is actually part of a 5-dimensional lattice.
So where exactly was the physics expertise of Kip Thorne used in this movie? Was it in the scene where sparks appear in the black hole, which rip the spacecraft apart but leave the spacesuit of the astronaut intact? Or was it in an earlier scene, when the spaceship takes off from the water planet? Supposedly gravitation was really strong there, so the rocket engines had to be quite powerful - but they left only a few ripples on the water. (Btw Newton's law of action and reaction was mentioned later.) This takeoff looked to me like a scene from Star Trek and I am talking about the 1960s tv series. And the earlier trip through the wormhole was Star Trek quality too imho.
Btw the whole sequence about Dr. Mann could have been cut out without any loss of precious quantum information, which would have accelerated the plot and spared us from watching Matt Damon's acting skills.
So here I am, left to wonder about the nature of space-time and in particular where those 3 hours went that I wasted with this movie. I am afraid that I will not find them behind my bookshelf.

the arrow of time in math

"... intuitionistic mathematics is an essentially languageless activity of the mind having its origin in the perception of a move of time. This perception of a move of time may be described as the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory."
Luitzen Brouwer

I can imagine somebody counting, beginning with 1 and then creating (more and more of) the natural numbers. But I cannot imagine the reverse process, somebody beginning with all of the natural numbers and then taking away one after the other. This is the main motivation for intuitionism in mathematics.

The platonistic view assumes that the natural numbers are "just there" as described by Peano's axioms. I guess platonism is the majority view among mathematicians.
Perhaps this division mirrors the two different approaches I mentioned in my previous blog post and the Grundlagenstreit was/is another instance of the debate about it?

the arrow and errors of time

We have memories of the past but not the future. It follows that we use probabilities much more often when we try to predict the future; e.g. a weatherman will tell us that the probability is 35% for rain tomorrow, he will usually not tell us what the probability was for rain yesterday (even if he is uncertain whether it was raining yesterday). The physicists say that this is just an example (and there are many more) of "the arrow of time".

At this point we have a choice.
i) We can declare that this "arrow of time" is a fundamental property of nature and indeed of (human) logic and move on to other topics.
ii) We can try to (and perhaps have to) explain or derive "the arrow of time", because the fundamental laws of physics are invariant under time reversal (with a tiny exception which should not matter for this point) and we have to assume that weathermen and our memories are composed of particles (and strings?) which follow those laws.

As far as I know C.F. v. Weizsaecker was the most prominent physicist in favor of i) and almost all other physicists follow the route ii), using the 2nd law and the assumption of special initial conditions for their explanation/derivation.

But the arrow of time is a tricky topic and not your usual empirical fact. Just try to imagine an experiment which would falsify it. The very existence of physicists debating it already requires this "arrow" or, as a proponent of ii) would argue, it requires a universe in an unlikely state far from equilibrium. This is one reason why there is still a debate about it.

If one is interested in this discussion I recommend e.g. H.D. Zeh's book.

Of course, this is a topic with many opportunities to talk past each other and confuse yourselve and others with circular arguments and errors. In other words, it is an ideal topic for the interwebs.

EBCDIC

The Soldier of Fortran explained recently how one can hack into an IBM mainframe. (Some of) his scripts are available here (interesting web design!) and if one scrolls down to TSHOCKER the main idea becomes quite clear. Btw many years ago I had to work with an MVS system, TSO, JCL and all that - so I find all this quite interesting.
How many mainframes are actually on the internet?
Quite a lot it seems and this web page lists some of them, discovered with a simple search bot.

a quantum of madness

At the top of the interwebs one finds Scott and his most recent blog post. The only problem I have with it is that it encourages me to think about crazy thought experiments and I already know they will not lead anywhere.

Btw I think there is one way to resolve the problem of conscious experience as posed by Scott, but one he would certainly not like: If there is a fundamental reason a large scale quantum computer (i.e. large enough to simulate a human brain) cannot work, perhaps along the lines of Gil Kalai's argument(s), and if the phenomena responsible for such a failure are associated with conscious experience, then every paradox could be resolved imho.

elaborate stories

"Today, Mirzakhani .. still writes elaborate stories in her mind. The high ambitions haven’t changed, but the protagonists have: They are hyperbolic surfaces, moduli spaces and dynamical systems. In a way, she said, mathematics research feels like writing a novel. “There are different characters, and you are getting to know them better,” she said. “Things evolve, and then you look back at a character, and it’s completely different from your first impression.” The Iranian mathematician follows her characters wherever they take her ..."
Quanta Magazine

Maryam Mirzakhani just won a Fields medal.


added later: The Austrian mathematician Martin Hairer is another winner. But he did not get the medal for his audio editing software, rather for his work on stochastic PDEs.
Terry Tao has a blog post about all the 2014 medallists.


added even later: It is quite interesting what Cathy O'Neil has to say about this.

Pluto and Charon ...



... as seen by the New Horizons spacecraft, which will fly-by next year.

sleeping beauty

Recently, Sean wrote a blog post about the 'sleeping beauty problem' and came out in favor of the 1/3 solution.
Naturally, Lubos had to respond with an obvious 1/2 answer and finally Joe Polchinski jumped in defending 1/3.

I wrote about this puzzle nine years ago on that other blog and people are still discussing it, because it has all the ingredients of a nice paradoxon: i) it is easy to calculate the probabilities and ii) there is an interesting ambiguity on how to use "probability" in this case, with the same outcome unknowingly sampled twice.

It seems that Sean honestly thinks that this ambiguity can be resolved using the many worlds interpretation, but I would point out that it actually supports Bohr's philosophy of complementarity: In general we cannot assign probabilities to a local object (in this case the coin), but we have to understand them in the context of an observational situation. In other words, the 'sleeping beauty problem' supports the Copenhagen interpretation.
8-)


added later: After re-reading my old post about this, I actually like the 3/8 solution.
Btw one way to undermine the 1/3 solution based on bet size (a la Polchinski) is to point out that the same bet size optimizes the outcome if SB does not fall asleep the 2nd time (but still has to bet twice the same amount). In this case the probability surely is not 1/3.

added even later: Joe posted yet another comment "which may make it clearer" why the correct answer is 1/3, while Lubos posted a whole new blog post defending the "obvious" 1/2 solution with an interesting modification of the original puzzle: Instead of just being put to sleep twice, with small probability 1/N 'sleeping beauty' is kidnapped by the CIA and tortured - waking up and put to sleep again and again N times; as N goes to infinity, the probability of being kidnapped by the CIA should go to zero.

added much later: Finally a commenter says what needs to be said about all this. It took long enough 8-)

a certain lack of entropy

Where we live one needs an AC, especially during summer. Our apartment is not that big, but we actually have two separate ACs, one for the ground floor and the other for the bedrooms. Unfortunately, they never manage to get to the same temperature (and humidity) - so when I walk up the stairway from the ground floor I can feel the temperature drop. And such temperature differences of about 1F can last for hours, long after the AC turned off.

But how is this possible? The air in our house is pretty much an ideal gas with some water molecules added and if I can walk through the stairway (there is no door btw) then the much smaller air molecules should be able to fly from one floor to the other too. The faster molecules in one direction, the slower ones in the other until equilibrium is restored, as we learn it in school. Furthermore, should the cooler air not quickly float down to the ground floor due to gravity or something?
In general, entropy seems to work fine in our house, e.g. when I spill coffee or drop something; but where is it when we need it?

Well, Sean Carroll explained to us that entropy is actually a cosmological effect and apparently it has to do with an "arrow of time". So I have to conclude that something is not right with the universe - and perhaps I should spend more time in the upper floor, assuming that the "arrow of time" is less pointy there? (*)


(*) added later: not really...

the pdf bang theory

"... a co-principal investigator for the BICEP team, acknowledges that the foreground map is an important and thorny issue. Part of the problem is that the Planck team has not made the raw foreground data available, he says. Instead, BICEP researchers had to do the best they could with a PDF file of that map that the Planck team presented at a conference. Moreover, Pryke says, conversations with members of the Planck team leave it uncertain exactly what is in the key plot. "It is unclear what that plot shows," he says."
sciencemag

I cannot believe this; one of the most important discoveries in recent years depends on a pdf file and it is unclear what it actually shows? Can the two teams please talk to each other and exchange the necessary data?
Jester was the first to report this story, but I think there is more than one jester involved in this ...

added later: Adam Falkowski explained the issue in more detail in a 2nd blog post.

elliptic curves

"... a major international scandal has engulfed some of the world's largest employers of mathematicians. These organisations stand accused of law-breaking on an industrial scale and are now the object of widespread outrage."
New Scientist

Tom Leinster writes about mathematicians having to decide if "we cooperate with the intelligence services" - his article is actually a pretty good summary of the NSA/GCHQ scandal.

How I became a solipsist ...

... it happened during a discussion on Scott's blog, in between here and there.
The real mystery is how 'the known' is embedded in 'the unknown unknown'.


-------

In totally unrelated news, we finally know how easter eggs are made ...



Happy Easter!

space roar?

"What was actually heard was something totally unexpected. Permeating the Universe was a strong radio hiss, about six times more powerful than anyone expected. No-one knew what it was or what was causing it. This was eventually christened "Space Roar" and remains one of the "Great Unsolved Problems in Physics"."
link

On my random walk through the interwebs I came across this article, which is low quality overall, but the space roar seems to be a real issue in radio astronomy - at least Wikipedia has an entry about it 8-).
I did not know about this "great unsolved problem in physics" until now, so please leave a comment if you happen to know more about it ...

can you have your pi and be in your pi too?

Scott reviews Max Tegmark's book about the many different multiverses and, as you would expect, a lot of deep thinking is happening in the comment thread.
Btw it is very likely that the best possible finite description of our world (e.g. all text ever written on wikipedia + arxiv + ...) and not just Scott's blog post, appears infinitely often in the decimal expansion of pi. The same is true for any randomly picked real number.
However, since there are infinitely many real numbers, it is also reasonable to expect that there are many which do *not* contain it even once (e.g. all the natural numbers).
A question for my smart readers: What fraction of the real numbers does not contain such a description of our world?

BICEP2

As I understand the news, BICEP2 has observed the effect of primordial gravitational waves in the cosmic microwave background, which is equivalent to a first glimpse of the GUT scale and in fact (indirectly) even quantum gravity (for more about it click here and there).
Or it has seen some instrument error(s) ...


added later: Lubos has a first evaluation of what it all means (assuming the observation is real) - just another example why I keep reading his blog 8-)

And this blog post has more about some issues with the reported data.

Congratulations Professor!

If I would have to write down what is great about the interwebs, Cosma's blog would be near the very top of my list.
But this is probably not the reason he just got tenure; He is a competent and innovative statistician and I never had much doubt that CMU would recognize that.
Congratulations!

Lubos Motl and the time travelers

Lubos Motl explains that he now likes "the idea that the 'spiritual proximity' is being geometrized by the recent realizations in quantum gravity". In other words, he thinks that "creatures with poor memory", e.g. bacteria, can be time travelers; We learn that "reappearances of the same bacterium are geometrically connected by bridges according to the (perhaps generalized) ER-EPR correspondence".

So when I get sick I could understand this as an invasion by time travelers, jumping around in the multiverse?
What about the cells which constitute my body?
While I try to type this blog post, the neurons in my brain are jumping through the past and future of the multiverse too?
Actually, I always suspected something like that ...

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