It is remarkable when you think about it. Put a pair of athletes on a field and give them a ball. After a bit of tossing it back and forth, one might throw it well past the other. Without using any equations she creates a model of its trajectory and starts it running as she turns from it and starts running down the field. At some point she knows when to turn, makes a few corrections to her position and catches it. Apart from the interesting sensor and computation problems there is the question of how accurate does she need to be? How bad can her mental model be and still allow her room for correction?

Knowing just where you are in position and time has been a traditional problem. For navigation it is relatively simple to calculate your latitude to reasonable accuracy with 15th century tools, but longitude was a different matter as the Earth is spinning on its axis. In 1707 this came to a head with a terrible naval accident that claimed four warships and perhaps as many as 2,000 sailors in British waters. It was later blamed on the inability to compute latitude accurately enough and it lead to the Longitude Prize of 1714 - an Act of Parliament that offered a then huge reward to anyone who could create a practical solution.

Clocks are still very important, but you need really good clocks. In fact the trick is to orbit and few dozen of them, each with a radio that sends out a time stamp and location. Your phone has an antenna, receiver and some computational power to receive some of these signals and quickly give you a mostly good enough idea of where you are.

The GPS system turns out to be simple in concept and difficult in practice. It is one of those problems that you would normally discount as just silly - too expensive and impractical - unless you had experience in navigation. A few years ago a few of us were asked to look at the problem of GPS denied navigation. There are any number of ways you might learn where you are and it makes sense to re-visit these periodically for certain niche applications (this was navigating in caves), but in the end if you can see the sky and the GPS constellation is operational, it is far and away the best solution.

An interesting feature of GPS is that relativity is turns out to make a difference. The satellite's speed with respect to a stationary point on Earth makes the time noted by the satellite slow by about 7 millionths of a second a day - just special relativity. But the satellites are farther from the center of the Earth than we are, so the general relativity tells us the clocks run a bit faster - about 45 millions of a second a day - these add up to a 38 microsecond per day correction and it is built into the location model along with corrections for radio propagation through the atmosphere, orbit determination and a few dozen other issues. The model is thorny and has enough understanding of applied physics that it works well enough for conventional navigation.^{1}

So Einstein was important to a critical piece of our defense and economy. But we rarely use special relativity in our normal lives. Frequently it is claimed that Special Relativity replaced Newtonian physics. It turns out special relativity reduces to Newton physics in the limit where objects are moving "slowly" with respect to each other. For most practical purposes we can just go ahead and use the simple mathematics of Newton. One theory augments another rather than replacing it.

The same can be said for quantum mechanics. What triggered the blog was hearing that Ken Wilson had died. Quantum mechanics is elegant, but also very strange to our expectations - a bit kooky as Feynman would say - but that's the way Nature works. When you get to a small enough scale it is time to throw out classical physics and use quantum mechanics instead. Possibly no one understood quantum mechanics more intuitively than Wilson.

Quantum mechanics happens to be very important for us - numerous bits of how our electronics work depend on a rigorous understand for example and it drives many physics processes at the atomic and even the molecular levels. But, like relativity, it has an influence in when you might think you can totally discount it. Recently a beautiful little experiment showed just that.^{2}

Now there are about a dozen directions I could go, so I'll just pick one and see where it leads.

A very interesting question is will new physical law replace relativity and or quantum mechanics and where will it be important? Both are difficult, but I suspect classical physics will be just good enough for 99.99% of what we do as humans for a long time. When you get to smaller sizes and much higher energies (temperatures) that we're used to you need to go to newer physics.

It turns out there are four known forces in nature - gravitation, electromagnetic, strong and weak. Three of them have been unified - the standard model was developed in the mid 1970s. There are bits and pieces to nail down, but it is a remarkably solid and predictive model. A problem, it turns out, is gravity.

Gravity may seem like a big thing to us, but we're pretty big at about halfway between the size of an atom and a star. There is a lot of mass in us and we tend to have problems falling on something as massive as the earth. But gravity is weak - astonishingly weak. If gravity has a strength of 1, the electromagnetic force has a strength of 1,000,000,000,000,000,000,000,000,000,000,000,000 (36 zeros if I counted correctly), the strong force is about 100 times stronger than electromagnetism. The weak force only has 25 zeros after it, but still ...^{3}

You've probably seen Feynman diagrams popular with particle physicists. They are a shorthand notation that buries a boatload of math and allows you to examine a large class of fundamental interactions - electrodynamics with some quantum mechanics and relativity thrown in. Usually time runs along one axis and position along another. Particles collide, forces are represented by squiggles and so on.^{4}

Imagine a particle that interacts with another particle through some force. The top diagram represents two particles interaction with some force f between them (if it was electromagnetic the squiggle would be a photon). One of the beautiful things about the theory is that if this is true, you can rotate the diagram 90 degrees and, if the energy is high enough in the collision between the particles labeled p, new particles labeled x are created.^{5}

This turns out to be useful. Physicists can do experiments and look for unknown forces. Perhaps the force is very very weak or it only works at very short distances.
The strange looking plot from a paper a few years ago that summaries searches for new forces (discover a new force and you get a Nobel out of it which can lead to amazing perks like reserved parking places). It is possible to rule out new forces in much of the observable world, so it seems likely at our scale that we will never see much of a modification of what we have. Any new force with a range on the human size scale would have to be more than 100,000 times *weaker* than gravity! Of course finding new forces, even though they apply to odd conditions, can lead to a deeper understanding of what makes the universe tick, so lots of good stuff remains.

t is interesting to thing that, at the level of human observation, fundamental physics is largely solved. That doesn't mean there isn't a huge amount of fundamental physics lurking out there, its just that we probably won't need the corrections for our daily lives. now, this sounds like an absolute statement and they tend to fall, but there is a lot of confidence behind this. There is also a huge amount of non-fundamental physics at our scale that needs to be done. Our understanding of even simple amounts of complexity is poor at a deep level. In theory we could work it out, but it is just too complex - we need new understandings.

This is a natural pivot to emergent properties, but time is out. sigh ... such a wonderful topic.^{6}

I strongly recommend finding a friend or your dog and playing around a bit with some simple classical physics. It may not be at the edge, but it is still amazingly fun and even seemingly simple things (like the biomechanics of walking) are yet to be sorted out.

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^{1} An applied physics discussion of relativistic corrections to GPS by Neil Ashby of the U of Colorado. It turns out there are deeper relativistic corrections that would be necessary if we wanted a more accurate system.

^{2} The introduction may give the impression this is new physics - it isn't. It confirms what is expected. This happens all the time in science. People figure something is too difficult to measure and move on to other things. Then someone comes along with real cleverness and/or better measurement tools and performs the experiment.

^{3} As an exercise calculate the electric force between the electrons in two gallons of water separated by, say, ten cm or so. It turns out to be strong enough that it could easily lift the weight of the earth.

^{4} I'm not being precise, but just to give a rough description.

^{5} Being really caviler on particles and antiparticles here. Generally think of a particle and its antiparticle colliding and creating another particle and its antiparticle..

^{6} It is wonderful to think that a room full of air molecules with someone on the order of 10^{30} equations that would need to be solved in the simplest possible case, reduces to a couple of equations due to an emergent property of scale.

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Recipe corner

The really good produce isn't here yet, so in the meantime this is a nice Summer soup that will improve as real corn arrives.

**Corn and Avocado Soup**

**Ingredients**

° 1 avocado

° 3 cups almond milk (could use regular whole milk if not vegan)

° 4 cups yellow corn (canned unless you can get it on the cob)

° 1 tbl finely chopped onion

° 1/8 tsp turmeric

° 1 tsp cumin

° some sea salt

° some freshly ground pepper

° coriander

**Technique**

° toss everything except the corn into a blender and blend 'til smooth

° add the corn and season to taste. If you like try running about half the corn through the blender for a different texture. You can also add chopped herbs if you like -- experiment!

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Bonus section

A WNYC *Soundcheck* interview of the director of the Macaulay Library's extensive audio collection - about 150,000 samples

An amazing resource!

Also recommended is The Great Animal Orchestra by Bernie Krause. I link to the iBook version which has higher quality audio than the Kindle flavor. Of course it should be listened to with good headphones or speakers rather the internal speakers to hear the detail. A downside is iBooks current doesn't work on laptops, although that supposedly chanages in a few months.

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