Thoughts about big questions

• Is math invented or discovered? This is not such an interesting question as we have no way to decide this. Both scenarios are possible and we have no tools to figure out which is right. It also depends on the precise meaning what we think to be the "inventor". A good answer was once given by Kontsevich at a panel discussion: "good math is discovered, while lots of invented math should be forgotten". Why can the question not be answered? If we were part of an elaborate computer simulation the rules would have been invented by a game designer. On the other hand if it would have be invented by us only, then it would not exist without us, which is silly too. Is the Pythagorean theorem gone, if humanity would get blown away by a solar storm? Or did it not exist 10 thousand years ago? On the other hand, that theorem could have been designed by a game designer and that architect would also have created the proof system allowing us to give a proof. In some sense we have wiggled us out of this system by creating non-Euclidean, Riemannian and non-commutative geometries already where the theorem needs to be modified, but these additional layers could all have been created too by the game designer to contain any ``smarty pant" trying to escape the game. This leads to:
• Do we live in a computer simulation? We have not noticed a glitch in the matrix yet! It would be depressive, if we would live in a game because you know that the kid playing it in a console could switch it off at any time. Camera zoom to a level up in the simulation: "Johnny! Dinner time!" End of game. You can imagine the game designer to have built nicely looking theories like string theory and laugh hard by watching humans follow the clues and see them get to nothing. We already have computer games which make one really believe to live in an other world. For me personally, this has happened already in primitive games like old Atari games or Myst or one person shooters. For modern games it is even more extreme. We can today explore Alexandria as it was 2000 years ago.
• Is math a tool for science? It is maybe more like that science is a playground for math. Math is widely seen as the universal language for all sciences but it is more: essentially all mathematical structures are also realized in nature somewhere. I used to tease my high school friends following biological sciences that physics is part of math, chemistry is part o physics, biology is part of chemistry, medicine is part of biology so that all is just math ... There is a famous XKCD cartoon which brings it to the point.
• Is there a god? It depends on the definition. If it is a concept like mathematics, yes, if it is an old man or women sitting in a cloud surrounded by angels, then I don't think so, even so we can not exclude it. It would be silly although. Also non-existence proofs are not convincing: "God is almighty. So, it can build a wall it can not climb, contradicting the property almighty." On the other hand, it is hard to imagine that just all is random. Completely random structures are not that nice. The fact that there exists interesting mathematical structures, allowing for complex systems to evolve is amazing. We could imagine a frame work, where every axiom system is inconsistent, not allowing to do any useful science at all. There are models in statistical mechanics which explain the emergence of nice structures from chaos. It is the emergence of language and logic which allows us to explore such pattern formations. Maybe the best answer to the question is given by Pantheism which is the point of view that everything including us is god. A measurable justification is that this word is one of the most common words used as passwords... This leads to a much better question:
• What programming language is the best Every language has its use. I personally like both high level programming languages like computer algebra systems as well as very low level programming languages like Turing machines. I myself program mostly in scripting languages (Perl, Bash, Javascript, Python) and computer algebra (Mathematica Example, Pari Example) and specialized systems (Povray, OpenCas, Processing), sometimes in fast compiled languages like C [Example: Chirikov, or Omnidirectional vision] or Pascal [Example: almost periodic sphere packings]. And then there are lots of languages that are border-line programming languages (even so many are Turing complete) like LaTeX, WebGL, Php, AIML, HTML, XML, SVG or Postscript in which it can be good to be fluent in. Additionally, it is useful to know well a few basic data formats like for picture, movie, music, styles. More important is the ability to translate between formats and if necessary to be able write a translator or driver. Sometimes it is useful for example to write down by hand each pixels of a picture as a .PPM file (containing triples of red,gree, blue values) [I did that for example for these pictures as it gives control about each pixel] or of reach triangle of an object as an .STL file (containing triples of numbers as well as normal vectors) with to be 3D printed. I often write programs which write programs for other languages. An example is Mathematica writing a javascript procedure which can be watched with a browser [Example] or a file which can be run through a ray tracer [An example] or Mathematica exporting an OpenScad program which appears in this article or then probgrams write themselves. Having recovered again from too deep questions, here is the next:
• What religion is the best? Pluralism takes the best of all religions. Especially holidays! Seriously, we don't have enough holidays. These are the times during which we are most creative. There is some correlation between religions with lots of holidays and scientific or artistic successes of that culture. Mathematicians often prove theorems during holidays (the prototype is the Christmas theorem in number theory which was found by Fermat in a letter of December 25th). So, if anybody will build a religion with the first amendment "You shall have lots of holidays", then I'm in.
• What method in science works best? Dogmas and methods are more like limitations. Rather than a method, we need fact checking tools to assess whether we make progress at all and not just build on sand. Any physical theory for example should relate to experiments (which can be mathematical thought experiments). Having been exposed to lectures of Paul Feyerabend (who also saw anarchism as a scientific method) as an undergraduate, I learned also to value the "no method" approach. But whatever works, works. If "method" works, let it be the "method". If chaos works, let it be chaos. What is more important is the ability to measure whether something "works". And that requires quantitative, rather than qualitative results. In mathematics, a theorem which gives equalities or estimates is much less likely to be false as a result which is not quantitative and just gives existence or worse, is speculation or hypothesis. A result claiming that a certain type of maps has three fixed points is a quantitative statement. It can be tested in examples. Quantitative statements are more reliable if they are constructive as again, we can see that things work. Also in physics, results which give quantitative measurable results are the most valuable. The gravitational wave measurements are one of the most recent examples.
• Is mathematics consistent? There should exists an axiom systems which is consistent. It would be depressive it would all be in vain. If every axiom systems was eventually inconsistent (meaning we could prove a false statement in each of them), we would have to retreat to nihilism which (quote from the movie Lebowski) is ``not even an ethos". ZFC most likely is. Even more likely is Quine's new foundation. Currently, Lawvere's elementary theory of the category of sets ETCS looks good as it is also flexible, allowing for example to work in a finitism framework. We know by Goedel, that it is not possible to figure out within a given axiom system, whether it is consistent. This is similar as that we can not figure out whether we are part of a computer simulation. It is turtles all the way round. Even if we would find a glitch in the matrix, the game designer having programmed it could be part of a simulation too.
• Are the multiverses? By definition, the universe is all we can ever access or which affects something we can ever measure. In the Wikipedia article about it, Newton is already credited with the idea but Newton made the observation that we can imagine different physics. And that is what happens in mathematics. We can simulate the Newton problem in any space in any dimension and analyze it, we can look at gauge theories in any space and dimension with any gauge groups, look at different versions of quantum mechanics or different string theory landscapes, or using different new mathematical structures. This is all great as it is math and that was what Newton already pointed out. In physics, if something should happen in an universe what is inaccessible to us is just not of any interest to us. ``Inaccessible" of course means that it has no measurable consequence for us, neither in the past nor in the future. The problem with the term is not so much the confusion about the definition but the advocacy to change in the point of view what science is. A much less reliable approach. The discussions about multiverses could be as pointless as the questions about whether we live in a simulation or whether the term "manifold" refers to a connected space or not (it is a pointless discussion as it is a definition). The topic however makes for some good science fiction or comedy. Maybe the entire thing is just a plot with the goal to entertain.