What is the most beautiful equation?

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What is one accomplishment you are most proud of?

Answer by David Dubov-Flinn:

In 1994, I was working at NASA's Jet Propulsion Laboratory as a secretary when a co-worker came to me one day to tell me about this new thing called the "Internet". He showed me a piece of software he called a "browser" and the amazing things you could view with it – including a group of pages from the project on which I was working, Mars Pathfinder.

I was fascinated, and spent the next couple of days dreaming of the things I could do. After obsessing over the sites I found, I went to my boss, the project manager, and asked if I could take over the group of 10 or so pages that one of the engineers had posted to the JPL server. While not exactly encouraging, he wasn't opposed, and let me do it with the understanding that it shouldn't interfere with my regular duties.

Over the next year and a half, I spent every spare moment teaching myself how to write HTML, how to manage a server, how to make pages that were visually appealing and had compelling content, and how to build it all into a coherent site. (Being a drama major, this was all new territory to me.) I also found time to write a newsletter about the project, too.

Needless to say, my secretarial duties were gradually phased out, with the approval of the boss and I took on the management of the site full-time.

I'd now managed to write, code and post about 1,000 pages of information, with photos, live video and audio streaming, time-lapse photography, and updates at least every day. (Keep in mind this was 1996…) The site was consistently getting about 2k-3k visitors a week.

(I won't get into the battles I had with the NASA bureaucracy about posting such volumes of information without going through the usual channels – suffice it to say that I took it all the way to the Director of the lab, and he backed me 100%.)

Eventually, I reached the limit of my technological and time-management capability and called in a software engineer to help me with taking care of the logistics of the site. Kirk and I did some very preliminary analysis of the traffic the site had been receiving, and with a big event coming up (the actual launch of the probe to Mars) we planned carefully for the number of visitors we should expect and what we would need to make sure the site was able to handle it.

1,000,000 visitors in one one day was just a *little* more than we expected! Needless to say, we went back to the drawing board and broadened our approach to site traffic and availability. We worked with other NASA centers and other countries' space agencies, and mirrored the site to 40 off-site organizations. Kirk wrote a script to automate the delivery of new files to the mirror sites. We called in robust servers from technology companies in Silicon Valley. We streamlined the site as much as possible, while still maintaining a rigorous update schedule.

By the time the landing on Mars approached, I had posted 10,000 pages of material, and we were as ready as we could be.

And on July 4, 1997 the Mars Pathfinder lander bounced down on the surface of Mars, and the little Sojourner rover rolled off its platform – the first mission to reach the Red Planet successfully in over 20 years.

The site was a smashing success, too, with 750 million visitors in 90 days (sometimes reaching 300 hits per second.)

I'm very proud to have built one of the first 1,000 web sites in the world, and to have been able to provide so many people with access to the mission I loved.

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How did a large fleet of ships communicate before mobile technology was invented?

Answer by Stephen Tempest:

In the early days, messages might be passed from one ship to another by shouting, or by sending a small boat to physically carry a message. Flags, lights or musical instruments might be used too, though in a fairly haphazard way. Often, the admiral in charge would gather his captains together before the battle for a council of war, and issue them instructions to follow during the coming fight. This might include agreed-upon signals to perform certain actions.

By the 17th century in Europe, fleets were growing much too large for such ad hoc measures to be practical. Standardised signal codes came into use, though at first these were quite basic. For example, the British Navy in 1653 issued 'Fighting Instructions' which specified that, for example, if the admiral hoisted a red flag on his foremast, it meant, "Attack the enemy fleet"; if he hoisted a blue flag from his mizzen mast it meant, "Follow me", and so on. If a ship spotted the enemy, they would warn the rest of their fleet by firing a certain number of cannons.

Over the next century this system became more elaborate, with many different colours of flags being hoisted at different positions on the ship to send different messages. Unfortunately, by the 1760s the system had grown  out of control; much too complex and illogical because it had been added to at various times for all sorts of reasons. The British Admiralty therefore introduced several different attempts to codify and rationalise the system. Nelson's famous signal at the Battle of Trafalgar, "England expects that every man will do his duty", was sent using one of these, the Popham Code introduced by Admiral Popham in 1800.

This was based around ten coloured square flags plus a number of additional pennants. Each flag could represent either a number, or a letter of the alphabet: so flag #1 also stood for A, flags #1 and #2 together, making 12, stood for the letter M (I and J were considered the same letter, and didn't have separate flags). Messages could therefore be spelled out letter-by-letter: but to speed things up, there was also a printed codebook which included shortcuts for common words. For example, the flags #2#5#3 flown together in that order stood for the word 'England'. Codebooks were secret, because of course the enemy could see the flags just as well as your own ships could – but they wouldn't know what each combination of numbers actually meant unless they broke the codes.

Warships of this era normally sailed in a long line, nose-to-tail – the "line of battle". This meant that the crew of a ship could only see the ships immediately in front and behind them. Signals would therefore have to be passed down the chain one by one – each ship hoisting the same signal as it saw the ship in front hoist it, until they'd all received it, This was naturally time-consuming and could lead to errors in transmission. It therefore became usual to have a 'repeating frigate' – that is, a small, fast ship would sail parallel to the line of battle but some distance away from it, on the side away from the enemy. Its crew would carefully watch the admiral's flagship, and repeat any signal it hoisted – the other ships in the fleet would be watching the repeating ship, and so would see any signal it flew straight away.

Flags were useless at night, so light signals were used instead. In Nelson's day they consisted of a square wooden framework hung from the mast, to which lanterns could be attached in various positions to make squares, diamonds, and other shapes. Firing guns and ringing the ship's bell could also be used to send signals, though this was far more limited than the flag code systems.

The semaphore system using flags held at different angles was a late development. France introduced a system during the Revolutionary Wars, with networks of towers with large mechanical arms and vanes on top to send messages across the country. This was soon copied by other countries. The idea of having an individual person holding flags in his arms and moving them around to spell out signals came later, in the 19th century. Once introduced, though, semaphore was seen to be more useful than the old flag code systems because it was much faster.

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What are some efficient designs for a tiny home?

Answer by Jordan Phoenix:

I created this design a few months ago using Google SketchUp. It packs everything you need for modern living into 126 square feet of living space.

Fully furnished tiny home for one comfortable person; could fit two in a squeeze

Shown in the picture:

1. Loft Bed
2. Shower
3. Toilet
4. Bathroom Sink
5. Kitchen Sink
6. Mini Fridge
7. Stove/Oven Combo
8. Washer/Dryer Combo
9. Microwave
10. Range Hood
11. Desk
12. Chair
13. Chaise Lounge
14. Kitchen Cabinets
15. Storage Chest
16. Water Heater
17. Heat/AC Wall Unit
18. Laptop
19. Mounted Flatscreen TV
20. Bathroom Shelves

Here is an estimate of the costs. It can actually be even cheaper by building the entire thing from scratch rather than buying the shell of the house (as I assumed in these cost estimates, because it was part of a proposal to a specific company who creates these mini house shells). In this instance, you'd need to consider the cost of walls, doors, insulation, base for the floor, tools to build, etc.

If anyone actually plans on building a prototype of something like this based off of the graphic model, I'd love to see a picture!

*Note: I personally don't believe that owning a microwave or television is necessarily good for one's health, and don't own them myself; but I put them in based upon what I thought would fall into the modern standard of living category to show that it is feasible to fit everything within the space. Plus, that mounted flat screen arm thingy kind of reminds me of something from the Jetsons, and makes the picture look way cooler. So yeah.

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How did WW2 Allied bomber formations keep from hitting each other with machine-gun fire?

Answer by Andrew Warinner:

The US Army Air Force developed the "combat box" formation for its heavy bombers that was designed to provide the maximum amount of protection.

The basic combat box was a four (later three) bomber formation that arranged the bombers both horizontally and vertically to give the clearest fields of fire for its machine guns.

Machine gunners in the various positions were assigned sectors; they could engage targets in their sectors but not outside of it as it risked hitting bombers in the box. And the bomber box was supposed to be tight: a tight formation meant that the bombers were within a wingspan or less of each other, not an easy feat when the bombers were buffeted by turbulence from other aircraft in the formation, flak and weather.

The most vulnerable bombers in the box formation were the "Tail-end Charlies." They had the fewest number of bombers and machine guns covering them and were consequently the preferred targets for German fighters.

As for the effectiveness of the .50 caliber machine guns that equipped US bombers, there is some debate if they were the best choice of armaments.

All the combatants in World War II quickly discovered that light machine guns like the .303 or the 7.92mm were not the best at shooting down aircraft. Fighters were equipped with a mix of light machine guns and larger cannon, 20mm and even larger and in some fighters machine guns were abandoned in favor of cannons only. The explosive shells fired by the cannon could carry farther and do much more damage but there was a trade-off: cannons had a much slower rate of fire and less ammunition could be carried.

The .50 caliber machine guns used by US bombers were better than the .30 caliber machine gun having a longer effective range and more penetrating power but still didn't match the 20mm cannon.

The US did experiment with mounting 20mm cannons in the tail gunner position of B-17s but did not deem it a success. Tail attacks were not preferred by German fighters since it was covered by the tail guns, ball turret guns and some upper turret guns in the formation. Manhandling 20mm ammunition back to the extremely constricted tail gunner position was not easy and less 20mm ammunition could be carried.

The effectiveness of the bomber machine guns in shooting down enemy fighters was fairly marginal. Bomber machine gunners consistently overclaimed successes by several times – fighter pilots did too – but this is understandable when several gunners might be shooting at the same aircraft. Commanders quickly learned to privately discount claimed kills.

The pure strategic ideal of self-defending bomber formations attacking heavily defending targets was proved unworkable in mid-1943. The US attacked a series of German industrial targets and suffered prohibitive losses. The raid on the ball bearing factories at Schweinfurt and Regensburg by 376 B-17s lost 60 bombers with up to a further 100 damaged against 27 German fighters shot down. This was an utterly unsustainable rate of loss and the US was forced to refrain from attacking targets in Germany until fighter escorts were available to fly the entire mission with the bombers.

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Renshaw Racing Killarnee

Renshaw Racing Killarnee by Team Navy
Renshaw Racing Killarnee, a photo by Team Navy on Flickr.

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How does the level of conscious attention to sensation affect its intensity?

Answer by Bradley Voytek:

Now we're starting to get into some of my research! Cool.

Let's say that I'm at a home listening to iTunes when I get a phone call from my wife. I'm a child of grunge, raised by a 70s father, who was into 90s rave scene, so depending on my mood I'm either listening to Alice in Chains, Credence, or Orbital. In any case, the music is way too loud and I can't hear my wife to save my skin.

In order to improve my chances of hearing her I have one of two options. I can either:

  1. Turn down the noise (pause iTunes), or;
  2. Increase the signal/gain (turn up the volume on my phone).

Of course, I could also do both, but that might be overkill.

This analogy applies to human attention as well. For whatever evolutionary reason, we humans have evolved with highly sensitive sensory organs with a very limited attentional bandwidth.

Just to give you an idea of how sensitive (see here for references[1]):

  • We can detect as few as 2 photons entering the retina. Two. As in, one-plus-one. Under ideal conditions, a young, healthy person can see a candle flame from 30 miles away. That's like being able to see a candle in Times Square from Stamford, Connecticut. Or seeing a candle in Candlestick Park from Napa Valley.
  • The limits to our threshold of hearing may actually be just above Brownian motion. That means that we can almost hear the random thermal movements of atoms.
  • We can also smell as few as 30 molecules of certain substances.

We appear to have a "processing bottleneck" however that prohibits us from simultaneously cognitively processing all that information.

To deal with this high sensitivity combined with low processing capability, our brains "filter out" a lot of the incoming information either directly sensory level or somewhere father along the neural network before getting into conscious cognition.

For example, most people think that when light enters our eyes that makes neurons activate. While true a little farther down the line, it turns out that the photoreceptors of our eyes are actually always firing action potentials (the main signals the brain uses to communicate) in the dark. When a photon enters the retina at the back of the eye, it actually causes the photoreceptor neuron to stop firing an action potential!

From a signal fidelity standpoint this makes a lot of sense even though it costs a lot in terms of energy to keeps these neurons "always on" in the dark.

Imagine again my iTunes scenario from above. Sure, if I turn up the volume (increase the signal) I will be able to hear my wife better, but there's still the music noise in the background. But if I turn down the noise by pausing iTunes, it becomes a lot easier to hear my wife even if I'm at the lowest volume setting on my phone.

In other words: it's easier for your "signal" to be the total shutting-off of noise than trying to amplify the signal above the noise.

The main theoretical mechanisms for how attention operates in the human brain to enhance a sensory stimulus is by shutting down/inhibiting competing stimuli and modulating the gain (making more sensitive) the sensory stimulus itself.

The brain appears to do both things. While we're not totally sure how

Over on my answer to Neuroanatomy: What are the primary functions of the dorsolateral prefrontal cortex? I talked about some of my research with people who have lesions to their frontal lobes.

It turns out that if I'm asking a person to pay attention to a certain part of their visual world and ignore another part, activity in the part of their visual cortex that represents the attended space is enhanced while activity in the part of their visual cortex that represents the ignored space is not (or is even suppressed).

Furthermore, patients with lesions to their prefrontal cortex (important for guiding attention, etc.) show altered activity all the way back in their visual cortex such that they don't show this attention-guided enhancement of activity. This is illustrated in the figure below from my 2010 PNAS study [2][3] that shows that patients with prefrontal lesions have high "alpha" activity (an index of suppressed functioning) in the visual cortex on the same side of the brain as their lesion.

There's even some evidence that when you need to pay attention to a specific auditory frequency–for example at the frequency at which your baby cries–the neurons in your ear that represent that frequency might actually physically move so that they respond more easily to that frequency [4].

Humans are incredible.

[1] http://blog.ketyov.com/2011/05/we-are-all-inattentive-superheroes.html
[2] http://blog.ketyov.com/2010/10/voytek-pnas-paper-prefrontal-cortex-and.html
[3] http://www.pnas.org/content/early/2010/09/29/1007277107.full.pdf
[4] http://www.ncbi.nlm.nih.gov/pubmed/22871520

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