A few days ago I was standing on a rocky Cape Cod beach at five am enjoying the starry sky. Slowly the dawn began to approach from the East and a nearly full moon was setting in the West. The sky was clear and stars down to about 4th magnitude were readily visible. A darker night would have produced a larger display, but it is amazing how many stars you can see and, at the same time be able to see the moon.
A rich experience like this makes you think about the wonderful dynamic range of some of our senses and the reason why our sensory responses are logarithmic.
Astronomy is saddled with a bizarre and archaic brightness measurement (you find really strange historical measurements throughout science) called magnitudes. A star might have a brightness of magnitude 1 with dimmer objects receiving larger numbers. Historical conventions give a few starting points which are now abandoned as the scale is tied to other measurements. The scale can be used for very bright objects like the Sun and moon. These bright objects have negative magnitudes as do the brightest stars and planets - Sirius, the brightest apparent star (brightness perceived by on Earth), is about -1.5.
So what is the dynamic range of the human eye? How much brighter is the brightest object you can see compared to the dimmest?
On a dark night with dark adapted eyes a person under 30 should easily see a 6.0 with some people in exceptionally clear areas going down to 7.0. Using binoculars or a small telescope allows you to see much dimmer stars, but let's stick with the naked eye.
One of the first rigorous definition of magnitude had a difference of 100 in brightness represented by a change of 5 units of magnitude. A first magnitude star is 100 times brighter than a sixth magnitude star. This implies a one unit change of magnitude has a brightness change of the 5th root of 100 - a bit over 2.5 (2.512).
A well placed full moon with a clear sky is -12.7 while the Sun blazes at -26.7 under ideal conditions. That means the difference is about 2.512(-12.7 - (-26.7)) or 2.51214 If you work it out on your calculator you get the Sun being about 400,000 times brighter than the full moon.
Most of us can see a 6th magnitude star on a really dark night, but someone with young eyes and great vision in a very dark area can go as low as 7th magnitude. Now the exponent is 7 - (-26.7)), so it is 2.51233.7 This is approximately big - about 3x1013 or 30 thousand billion times!
Sweet, eh? Your eyes are fantastic instruments!
You can perform a similar exercise with your hearing. We can hear very loud (and damaging!) sounds. Our perception of loudness is not linear, but is closer to the power of the sound raised to the one third power. If you increase the sound level by a factor of ten you will perceive it is 101/3, or roughly two times, louder. The units are decibels (dB) and the quietest sounds a human can detect are roughly 0 dB.1 At the other end of the scale is pain, which is about 140 dB. These are separated by 14 orders of magnitude in power! - 1014 is an incredible range but, oddly, is close to the range of brightness the eye can handle.
In addition to our sensitivity to a range of brightness and acoustic levels, we are sensitive to different wavelengths of light and sound.2 Normal human vision is sensitive to electromagnetic radiation with wavelengths between about four tenths and seven tenths of a micron - about a hundredth the diameter of the thinnest blonde human hair.3
This three tenths of a micron range of wavelength gives us a tiny window into the electromagnetic spectrum. Our brain interprets the shortest wavelengths we see as red - light with a somewhat longer wavelength is called infra-red and even longer wavelengths become microwave and then radio waves. At the other end of the scale we have ultraviolet light - the stuff that causes sunburns. As the wavelength decreases we move to X-rays and finally to gamma rays.
The range of wavelength is amazing. AM radio, by no means the longest radio waves we deal with, are as long as skyscrapers are tall. FM radio is close to the height of a human, wifi waves are about the width of your hand and X-rays get down to atomic dimensions with Gamma-rays coming in even smaller.
But it is even worse than that. Our eyes and ears do not deliver a perfect rendition of the information that falls on them. It turns out a lot of filtering takes place - it has to as the amount of information around is is vastly larger than the path from our senses to our brain can handle. We have a very effective filtering and compression - think of it as image and sound compression along with compressions of the other senses. Much of this has a complex bias and the reality we sense is a construction of our brain. Concepts like color, sound and music are completely manufactured and interesting quirks can be probed with carefully thought out experiments and illusions.4
I don't mean to detract from the impressive instrumentation kit we are born with - it is mind wobbling beautiful - but we can get a much better sense of the real universe around us by building instruments and recording information with well understood biases. Every time we come up with a new generation and type of instrument we open new richnesses in our understanding the Universe - we build this sort of apparatus to fuel and guarantee the inflation of our collective ignorance. The telescope and microscope gave us enough of a change in perspective that we were able to fundamentally alter our views of the Universe as well as life itself. Our window to the Universe has many more dimensions than just light and sound. Consider the fact that our sense of time is highly constraining. Now we can witness events that take millions of years as well as those that take place in a billionth of a billionth of a second. We are even taking steps to understand things about our world and the Universe that are too large to appreciate - we are building computational macroscopes. We are beginning to build synoptic instruments and techniques.
You can enjoy the richness of a slightly expanded window with a pair of binoculars. The clearest regions of the planet can rarely show more than 2,000 stars to someone with great vision. A pair of 50mm binoculars extends your range down to about magnitude 10 on a wonderfully dark night. Now you can see a few hundred thousand stars and you will be doing better than Galielo Galilei did when he rocked our notion of what the Universe is. It is far and away the cheapest way to expand your window on the universe I know of. Try some time lapse photography with your digital camera and watch a cloud or a flower bloom. Buy a filter and try some infrared photography.
I won't dive in here, but our perceptual filtering is incredibly important. I have spent a fair amount of time studying out of band communication - the part of human communication that is not carried by simple representations of voice and even video. One of the things that is emerging is we, actually women, sense slight changes in shades of red very well and the amount of blood just under the skin - something that can depend strongly on health, nutrition and mood - is an important signal. The problem is the video cameras and monitors we use are incapable of conveying this level of detail. Audio is also poorly recorded and reconstructed and some important face to face elements are lost. Our minds compensate of all of this, but mistakes are frequently made.
1 It is too easy to get very technical here as our ears respond different as a function of the frequency of the sound. For example the quietest sounds most of us hear are around 3,000 Hz. The response drops on either side. At 10 kHz it is about 20 dB less - about 100 times, and at 100 Hz it is roughly 40 dB down - about 10,000 times. Our response drops naturally and even dramatically with age and abuse. Don't turn up that iPod!!
An interesting factoid is the the ear drum physically vibrates in response to the regular changes of air density that we interpret as sound. At the quietest levels the membrane is moving roughly the diameter of a single molecule. This is a rather exquisite instrument to say the least.
2 I use the term "sound" loosely. Technically our mind creates sound from the interpretation of variations of acoustic waves - regions of different pressures that travel as waves in the air at the speed of sound. It is a definition, but it is possible to say that sound doesn't exist without an ear and a brain to interpret it as sound. If you buy this a tree that falls unwitnessed in the woods has no sound - just acoustic waves that radiate out....
3 A micron is a millionth of a meter. Fine blonde hairs are about 40 or 50 microns in diameter with thicker black hairs going up to about 200 microns. The finest elements in an integrated circuit are a bit under two tenths of a micron - or about half the wavelength we call violet - the shortest wavelength light we can see.
4 It is amusing that some video and audio purists prefer "unaltered" and analog signals when the senses produce and the brain processes very limited and abstract representations of reality.
First a quick non-recipe that is so good now that amazing apricots are available. Cut perfect apricots in half (remove the pit of course:-) and dust with a bit of fresh lemon juice, lemon zest, vanilla bean sugar (I make this with old vanilla bean pods and regular white sugar). Put on a baking sheet in a 350° or 375° oven and roast until the apricot flesh gets a bit soft. The result can be pretty amazing.
And now an idea that struck. I was looking at some cherry tomatoes and wondered how cherries would go with tomatoes. Perhaps tart cherries with an heirloom tomato...? So I decided to see if I could make a gazpacho based on some of the tart pie cherries I have and a tomato. It was clear it needed cucumber, some garlic, stale bread, oil and so on - so here is the first try.
It is really delicious!! I won't change it much the next time around.
° 1 cup of pitted tart cherries
° a small piece of not terribly fresh whole wheat bread
° clove of garlic
° 1/2 garlic clove finely chopped
° a bit of olive oil or butter
° a half tomato peeled and chopped (I blanche them first to make the peeling easy)
° a small cucumber peeled and chopped
° 1/2 tsp chopped jalapeño
° 1 tbl vinegar (I used red wine)
° sea salt and ground pepper
° 50 or 60g or a couple of ounces of sour cream. (optional - it is plenty good as is, but this can add a bit)
° Remove the crust from the bread, rub the clove of garlic into the pores and fry the bread in a bit of olive oil or butter until it begins to crisp. Alternatively you might start with garlic bread, which is what I was trying to simulate
° Combine the cherries, tomato, cucumber, jalapeño, vinegar, garlic fried bread, and garlic and blend with an immersion blender or put in a regular blender. Season to taste with salt and pepper. Refrigerate
° To serve divide the gazpacho into bowls and add a dollop of the sour cream into each bowl. You could top it with nice looking herb leaves or whatever. I used a few blueberries and chopped pecans.