I spent a few days in Olomouc, the historical and religious center of Moravia, with a goal of giving a talk about the continuum and discontinuum at a summer philosophy school in the nearby Oakwood Upon Morava ("Dub nad Moravou").
If this blog were like Asymptotia.com, you would be offered some 284 blog posts with pictures of that area, the churches of Olomouc, the impressive pilgrimage Holy Hill ("Svatý kopeček") with the huge basilica where John Paul II gave a mass and led a pop music concert some 20 years ago, with a house where a famous Czech poet Jiří Wolker has lived. (I liked this non-distracting area with big things, it had a similar spirit as D.C.) The zoo was larger than I expected – lots of animals. No one told me that this tiger was a nervous CNN journalist who didn't like the cat game (what else should I have been playing with him?) so I had to wrestle with him in the same way as Donald Trump but I survived. ;-) Honestly, if I didn't tell you about the glass in between, it would look like one of the "Darwin's award" videos with someone's stupid death, right?
The talks on my day were about the relationships between the continuum and points, whether the non-constructible or non-algorithmic numbers on the real axis (which are those that make the continuum uncountable) "exist", whether they are fundamental etc. Well, some big picture conclusion of mine has always been that the specific, "algorithmic" numbers (which are countable) are at least more useful or more important and the others only "exist in some academic sense" in order to make an axiomatic system simpler. And there are various detailed axiomatic systems. All consistent ones are OK enough and more far-reaching statements should better be made rigorously and they may sometimes depend on the axiomatic system we pick.
My talk focused on whether or not the fundamental structures in theoretical physics are continuous or discrete. I began with Pythagoras' continuous (geometric) and discrete/rational (music, arithmetic) interests, Zeno's paradoxes, post-Newton centuries o straightforward differential equations where "everything" was continuous. Quantum mechanics was the serious topic. I argued that equations remain continuous because they determine the evolution of probabilities or probability amplitudes which are continuous even if they describe discrete outcomes. There are relationships between discrete and continuous objects, e.g. bases of a Hilbert space (the Fourier transform was the simplest example).
I discussed the monstrous moonshine as a great example of a truly surprising relationship between two very different mathematical issues – one of which looks much more "discrete" than the other, "continuous" one, I argued for the importance of continuous symmetries for the life to be possible, for the laws, to be constrained, and I ended up with criticisms of attempts to build everything on base-two system (natural logarithms and exponentials are the natural ones), and of discrete theories such as the cellular automatons and loop quantum gravities. Lots of post-talk discussions in the pub were about the algebraic geometry – the physicists' vs mathematicians' perspectives, on the stringy landscape and why string theory is considered progress from the predictive viewpoint, and many other things including climate change etc.
It's my policy not to try to revisit and cover details of traveling, events, and discussions from the real life – it would mostly be time-consuming and perhaps boring for the typical reader.
There have been numerous events in the world that took place in the real world in recent days as well. Trump has rightfully beaten CNN with his fists, as I have mentioned. Stephen Hawking has said another breathtakingly stupid alarmist thing – Donald Trump is a devil who will turn the Earth to Venus with its more intense greenhouse effect. Please, Dr Hawking, think twice before you make a complete clown out of yourself among all people with the IQ above 90. Venus has some 4.6 x 1020 kilograms of CO2 in its atmosphere. The Earth has less than 3 x 1015 kg of CO2, some 150,000 times less than Venus. An important politician of one of the largest countries may make decisions that add or subtract some 1% of the existing CO2 over his term. So the question may be whether Venus will contain 150,000 or 150,150 times more CO2 than Earth, not whether they will be similar, and your suggestion to the contrary, Dr Hawking, seems like an effort to turn yourself to a favorite "intellectual" of the most hopeless idiots on the Earth who love to be terrified like little kids. It's just a tragedy that a man who is arguably the world's most famous physicist according to the ordinary people is saying utter rubbish like that.
OK. Congratulations to the Americans whose country was declared independent on July 4th. This independence was successfully defended by the citizens of the U.S. in statu nascendi despite the wishes of a part of the international community; the U.S. wasn't "created" by the international community. Today, it's been exactly 10 years from my evacuation flight from the U.S. to Czechia – July 4th was the only date in the post-visa-expiration week (when I was obliged to leave America) with some available air tickets because Americans are (perhaps partly justifiably) afraid of the higher risk of terrorist attacks on the Independence Day. I am saying it as an example that shows that some "big accidents" (like the agreement between the two dates) are often not quite coincidental because there exists a bias that makes the agreement more likely than a uniform distribution would predict.
The grey ball in the middle could have been called a speculation 5 years ago. Now it's a member of the family of elementary particles whom we know as well as others – in fact, we have played with him much more than with others during the five baby years.
Also, today, it has been exactly 5 years from the day when the Higgs boson was officially discovered in 2012. It's plausible that the agreement with the Independence Day isn't "quite" a coincidence, either – the CERN folks may have wanted to pick a more memorable date and take some credit for the American fireworks. Five-year-olds are still handsome but be ready, Higgs boson, that things may get worse after 40 more years. ;-) (Even though, it occasionally happens that even impartial MILFs in a Moravian zoo trains kids may scream something about a handsome man LOL.) The Higgs boson around 125 GeV was a sure thing since mid December 2011, among those who evaluated the evidence as sensibly as I did. The Higgs mass became the last truly important parameter of the Standard Model that was measured and the Higgs-related processes were the last important ones to be discovered.
The fact that the Higgs mass isn't far from its vev, some 246 GeV, and especially that it is lighter than 1 TeV is guaranteed by some rather rigorous analyses e.g. of the possible formulae for the WW scattering. However, the better-than-rough proximity may also be considered a success of the naturalness. And as the first fundamental scalar field, the Higgs boson may be viewed as a victory for string theory that predicts numerous important scalar fields (although most of them are predicted to be heavy at the end – the lightness of their being is unprotected and therefore unbearable, thanks to Milan Kundera for some help with this sentence).
Back in July 2012, I won a $500 bet thanks to the Higgs because the Higgs particle simply had to exist. Lots of people discussed particle physics in the chat box when the discovery was being announced. Even in 2017, you shouldn't forget that other physicists, especially including the living Francois Englert who shared the Nobel prize with Peter Higgs, contributed to the theoretical discovery half a century ago. And due to some stability issues, the observed Higgs boson mass may be marginally incompatible with the pure Standard Model – although the very fact that it seems to be so close to the tolerable edge may have a deep explanation (e.g. some approximate conformal symmetry at a high energy scale).