Higgs Boson Buzz

It's buzzing in the media, on Twitter, everywhere. It will be announced tomorrow. The God Particle. It exists after all...

Here is a great animation about how the Higgs Boson particle works.

What is the topology of the universe ?

Do we know what the topology of the universe is? Is it possible to determine? By us, I mean. - Some thoughts, nothing more.

I think that most people think about the physical universe as one huge cube or sphere, filled with space-time, dark matter and dark energy, like the air in a balloon. The air of that 'balloon' however is polluted with billions and billions of galaxies. Somewhere in that balloon is our tiny earth from which we are observing everything and making smart conclusions so that we finally became able to understand the universe from its inception: the Big Bang. We even know what will happen to the universe in a few billion years. It's hard to check whether there has ever been a Big Bang. ( Physicists working in branches where results are verifiable are very modest. Think about weather predictions, and engineering another moon-mission: it would take decades. )

In popular science documentaries they bring us to 'the end of the universe', show us pictures of stars in faraway galaxies in extreme quality. How do they do that? It's not that the pictures are sent to us from that remote galaxy, they are taken from Earth('s orbit). Basically, data is captured, analyzed and processed. From that data a picture is generated: call it "probabilistic photography". ( It helps funding research if you can show some beautiful animations or pictures. What they really have though is a database with numbers. )

Physicists speak with authority and certainty about the Big Bang and the topology of the universe. That certainty is a pose, absolutely nothing is certain in physics.

I got kicked out of class once. Because I kept asking the physics teacher about gravity. "What -is- gravity?", ( I honestly didn't know that he couldn't have a clue at that time. ) I asked, when he started again about the g. constant. "Sir, -why- do objects fall to the ground?" Finally, he literally kicked me out of class.

To the point. I made two images.

Imagine that this is an abstraction of what we really know about the universe. The following image shows the same objects but from another viewpoint.

What is our viewpoint in relation to the vastness of what is around us? Does the topology of the universe permits us to see it all? Is the topology of the universe like that balloon or is it, perhaps, some topology not even discovered in the realm of mathematics? Would we ever be able to determine that?

Compare us with little intelligent tiny fish on the bottom of the ocean 'studying' the(ir) universe. What would their conclusion be?

Fabric of the Cosmos

I think I finally 'get it'. That space-time is not just a word, but a fabric. The fabric of the cosmos.

PBS did it again. They created a documentary you'll still be talking about in ten years time. If that sounds strange, think of the documentaries of Jacob Bronowski, Carl Sagan and Marcus du Sautoy.

Anyway, fabric of the cosmos is running now on PBS. Don't miss it.

"The Fabric of the Cosmos," a four-hour series based on the book by renowned physicist and author Brian Greene, takes us to the frontiers of physics to see how scientists are piecing together the most complete picture yet of space, time, and the universe. With each step, audiences will discover that just beneath the surface of our everyday experience lies a world we’d hardly recognize—a startling world far stranger and more wondrous than anyone expected.

Neutrino's supposedly faster than light.

Off-topic:

Neutrinos Travel Faster Than Light, According to One Experiment

I got really excited when I read that "... particles had been found that travel faster than light ...". ( local teletext ). Wouldn't that be amazing? I mean, all the major scientific discoveries seem to have been made in the distant past. ( Physics and mathematics, I mean ). That would change overnight if Einstein's law of relativity got broken.

My guess? A measurement error. They are talking about a particle that traveled 60 nanoseconds faster than expected. One nanosecond is 1/10^9 part of a second. I am sure they have found some ingenuous way to measure speeds involving figures like that, but NOT when the figures depend on GPS! Come on, GPS.

I am afraid that this could turn into something very, very embarrassing for CERN. I hope their P/R people are as brilliant as the scientists they employ. ( Except the guy who was -?- responsible for measuring the speed of neutrino's, of course. )

What is the dimension of color ?

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics.

Benoit Mandelbrot

The prototypical fractal

( I'll continue with my 'watch notes' of the GEB series later this week. But I'll stay on topic with this post. )

Imagine a recursive process which goes to a certain depth until it stops. This 'certain depth' is a natural number which can be assigned a color. This is basically how fractals like the one above are built, pixel by pixel.

Programming 3D graphics can get quite realistic as we all know from watching movies or playing computer games. What is this reality? When does a picture look real to you? It is what made Rembrandt famous, I suppose. Control over light and thus color and shading.

What I am trying to say is that one number is not enough to encode a color. This is rather counter-intuitive, I know, but only if you assume the number of colors is finite or countable infinite. How many colors are there? Finitely many? Countable infinite many? Or not countable infinite? I don't know.

Assume a scene with an object with a certain color, say lime green. This can be coded with one string, the RGB color method uses 32 CD 32 ( Hex ) for lime green. But then you have an object that looks exactly the same everywhere. Because there is no light in the scene. By adding light we have to add the exact location of the light source in the scene. Shadows must be calculated. And light will be reflected. Each pixel will have a reflection vector which has effect on the color. Does this add to the dimension of the color? What if there are other objects in the scene? They partially reflect light and thus become a light source as well.

Do you get the idea? Then what is the dimension of ( the vector needed to encode a ) color?

More:
- The Dimensions of Colour

GeomagicSquares

Magic squares + Geometry = GeomagicSquares, a concept created by Lee Sallows. Fascinating stuff.

I watched the BBC Horizon documentary "What is Reality?". Lots of interesting food for thought. About the race that is going on between CERN and Fermilab for finding the Higgs-Boson particle for example. A fundamental particle that supposedly explains the creation of mass. Therefore alone the particle is badly needed as it's a bit silly that almost every physics formula has mass in it but mass itself can't be explained.

The laws of physics can be described best with mathematics. Deep physics however can -only- be described with mathematics which leads to the thought that mathematics is not an invention but a discovery. In that sense research mathematicians are much like archaeologists.

[Review] - Atom 1/3 : The Clash of Titans

The Clash of Titans ( Atom 1/3 ) by Professor Jim Al-Khalili is a documentary about the birth of quantum mechanics. - According to Al-Khalili the discovery of the Atom is the most important achievement in science, ever ( amazing how every scientist says something like that about his or her field ). I wished he hadn't said that in the documentary itself because besides that Atom is one of those documentaries the BBC is world famous for ( starting with The Ascent of Man with Jacob Bronowski ). The program is educational, the photography is in one word beautiful and Al-Khalili is a real story teller, he turns the birth of quantum mechanics into an action movie with heroes, winners and losers. Atom was first showed on TV in early 2008 when I missed it but I have been able to pick up a copy of the entire three part series recently. With MST209 scheduled for next year more posts about physics will be inevitable, I suppose.

Math and physicists (2)

A while back I asked why physicists know so much math. In this video Prof. Ramamurti Shankar from Yale University teaches differential equations.

We solve DEs by guessing.

I like to watch science documentaries, since I have seen all Horizon and other channel's docs on physics by now ( some of them even twice or more ), I watch introductory physics stuff instead. Prof. Shankar lectures in an entertaining fashion.

Introductory Physics video.

How come physicists know so much about mathematics?

Although I am somewhat of a Science Fiction fan ( 2001: A Space Odyssey? Yes!, Star Wars? No! - Moon? Yes!, Avatar? Not really. ), I am illiterate in the world of science which is largely based on quantum mechanics. By choosing the right modules ( i.e. MST209, MS326 ) in my B31 track I'll be able to read and study quantum mechanics texts soon though.
I often wondered why a B.Sc. in physics has learned so much more about mathematics than what's in an undergraduate mathematics program. Is mathematics simple, easy, even relaxing compared to physics? It certainly seems that way. Well, seemed, for me anyway. I think I understand it now.
Undergraduate physics books are almost self containing with regards to mathematics. Mathematics is the language of physics enabling them to solve all sorts of problems. ( I am not surprised that innovations in physics were carried by the introduction of new mathematics to the field. Since they aren't trained in developing new mathematics they are also constrained by it. ) Large quantities of math are pumped into their brains without proof.
This video illustrates my point. It is lecture 3 from the MIT OpenCourseWare Physics I course.

This lecture is about vectors and how to add, subtract, decompose and multiply vectors. Decomposing vectors in 2 (or 3) dimensions is a key concept that will be used throughout the course.