[Jimbee (OP)]

Black absorbs all colors. White reflects them all. So what is gray?

IANAScientist. But what I described above seems to be opposites. And gray is black plus white.

So what is gray?

[varsigma]

try this:

imagine a line of grey between black and white. What is the intensity of black? of white? Does the intensity of either vary along the line?

[alancalverd]

  Grey is our perception of a low intensity normally-weighted (i.e. white) visible spectrum. It is necessarily a relative concept: the dark adapted (scotopic) eye will perceive some stimuli as grey that would be considered black by a photopic eye or if seen in contrast with a brighter white.   

[evan_au]

The Moon reflects about 14% of the light falling on it (albedo=0.14), so you could say it is grey/gray.
- A body which reflected 100% of the light falling on it you would call "white"
- A body which reflected 0% of the light falling on it you would call "black"

https://en.wikipedia.org/wiki/Albedo#Optical_or_visual_albedo

[vhfpmr]

The Moon reflects about 14% of the light falling on it (albedo=0.14), so you could say it is grey/gray.
- A body which reflected 100% of the light falling on it you would call "white"
- A body which reflected 0% of the light falling on it you would call "black"

https://en.wikipedia.org/wiki/Albedo#Optical_or_visual_albedo

What the brain thinks is black and white is all relative:

With a TV switched off, the unlit CRT looks grey, but when it's switched on the same areas look black when they're unlit.

Photographers use an 18% grey card for exposure metering, because a surface with a reflectance of 18%, not 50% appears mid way between black & white.

[evan_au]

a reflectance of 18%, not 50% appears mid way between black & white

For a lot of human senses which need to span many orders of magnitude in intensity, the response tends to be logarithmic, rather than linear (linear would imply 50% is half-way).

If we call White 100% reflectance, the geometric mean of white & black is the square root of their product,
- For a geometric mean of 18%, the reflectance of "Black" would need to be around 3%
- Reasonable for a very black card in sunlight (but modern TV screens claim contrast ratios over 1000:1 - in a very dark room)

PS: I think that kids would find maths and science more relatable if we talked in units they can feel - logarithmic units
- Sound intensity is measured in dB (logarithmic), sound frequency is measured in octaves (logarithmic), brightness in astronomy is measured in magnitudes (logarithmic), and hardness is measured on Moh's scale (logarithmic except for diamond)
- I suspect that things like touch, smell and taste would also have a logarithmic response
- Psychologists have even shown that abstract concepts like "value" or "wealth" also have a logarithmic response
- The Metric System and Scientific notation are both based on a logarithmic scale

I might write up some ideas on this when I get some time...

[alancalverd]

I published a note a few years ago, proposing a logarithmic scale of risk. It's clear that most folk are unable to decide whether a 1 in 1000 or a 1 in 1 ,000,000 risk of death is acceptable, but are happy with Beaufort wind scales (you would think twice about walking in a 6 or 7, but Force 4 won't stop you shopping) and Richter earthquake scales, so I proposed a risk index R
R = 10 - log P 
where P is the probability of something bad happening.
The inevitable (P = 1) has R = 10, and if R = 0 (P = 10^-10) then no living person is likely to observe it.
It turns out that folk generally tolerate R ≤ 4, expect some form of statutory regulation where R > 5, and consider R > 8 to be unacceptable. 

[Bored chemist]

If you include the facts that people tolerate risks that are common but don't kill many (like car crashes), rather than risks that are rare but do kill a lot of people (like plan crashes) (even when the expected total death toll is the same) and the fact that people accept much greater risks if they feel that they are part of the decision making process, (Which is part of teh reason why people argued against seat belts) rather than a risk imposed on them from outside, and the fact that people put up with greater risk where they see greater advantages ("Danger money" is illegal, but practically speaking it still happens) then you will have more or less caught up with what was known 20 years ago or more.

https://www.hse.gov.uk/enforce/assets/docs/r2p2.pdf

[evan_au]

On the related question of "What is Black?"...
I got a Christmas present: a tear-off calendar with a brief science story for each day.

Catching up after my summer vacation, the story for January 9 was about black bird feathers.
- Apparently, some birds of paradise have "ultrablack" feathers, absorbing 99.95% of the incident light. Electron microscopy revealed feather textures which enhanced light absorption.
- However, the feathers of "normal" black birds (I assume crows and ravens) absorb only 96.8% of the incident light.

This 96.8% absorption is coincidentally close to the 3% reflectance that I guesstimated in the back-of-the-envelope calculation above for "Photographers Black".
- if "Photographers Grey" is 18% reflectance, then "Photographers Black" is (18%)² reflectance = 3.2% reflectance = 96.8% absorption.
- After all, who takes photos of objects on Earth which are blacker than the feathers of a crow or raven?

[evan_au]

Stackexchange discussion on 18% grey:
https://photo.stackexchange.com/questions/62307/why-is-18-grey-considered-to-be-in-the-middle-for-photography

I was interested to learn that the characteristic of video cameras and video monitors are calibrated for a "gamma" of 0.5.
- This means that for 8-bit video (pixel intensity range 0-255),  the "middle" value of 127 corresponds to a brightness of 18% of maximum.

A speculation was that film cameras can handle exposures over about 5 f-stops (logarithmic scale). The 18% grey standard developed for film cameras is around the middle of a 5 f-stop range.
- Digital cameras can handle a slightly wider dynamic range than film cameras, and apparently some are calibrated for 12% grey (implying about 1.4% reflectance for black)
- The human eye can resolve 10-14 f-stops (with a fixed pupil size)

[vhfpmr]

For a lot of human senses which need to span many orders of magnitude in intensity, the response tends to be logarithmic, rather than linear

Any measurement that spans multiple orders of magnitude needs to be logarithmic: try designing a filter with 80dB of stopband rejection with the network analyser switched to linear, or transmitter harmonic emissions using a spectrum analyser on linear. Electronic component preferred values are a geometric progression, component tolerances are also in geometric terms (tolerances in mechanical engineering generally aren't, but you don't usually see bolt sizes in the same piece of equipment varying by orders of magnitude).

On the other hand, bicycle gears only span about 6:1, but they're also a geometric progression, they feel all wrong if they aren't.

- Psychologists have even shown that abstract concepts like "value" or "wealth" also have a logarithmic response

When it comes to money, people can be paradoxically geometric in their thinking when an arithmetic view is correct. It's been shown that people who would travel to get a 50% discount off a ?500 telly wouldn't travel the same distance to get a 1% discount off a ?25,000 car, even though it's the same benefit to their bank account. On the other hand, banks will round ?10.001 to ?10, but I bet they wouldn't dare try rounding ?10,001,000 to ?10,000,000

I published a note a few years ago, proposing a logarithmic scale of risk.

It isn't really practical to objectively quantify risk, because risk isn't objective.

It's plain obvious that:

different people have different appetites for risk,
people will act to re-assert their chosen risk level if others attempt to change it,
people don't want zero risk (and yet virtually every risk debate starts from the premise that they do),
there's a cost-benefit analysis involved in assessing and choosing risk,
people behave more carefully when they perceive more risk,
such changes in behaviour affect the risk,
people are many times more sensitive to a risk/cost imposed upon them by others than one they choose for themselves
people are more sensitive to a risk/cost imposed on them than to the same risk/cost when they impose it on others

...and yet people will fight tooth & nail against all this, and evidence supporting it, if and when it contradicts their own behaviour.

If you include the facts that people tolerate risks that are common but don't kill many (like car crashes), rather than risks that are rare but do kill a lot of people (like plane crashes)

Cars kill ~1500 Brits a year, I don't think that many are killed by planes, what's in operation is the Availability Heuristic: people perceive probability according to how easily something springs to mind. The spectacular which gets plastered all over the media at frequent intervals is more salient than the mundane which hardly gets a mention, regardless of the true probability.

[alancalverd]

It isn't really practical to objectively quantify risk, because risk isn't objective.

Oh yes it is. Risk is the product of probability x impact. In most cases involving damage to humans we can ascribe an impact value of 1 to death and turn to the insurance market for a consensus of "partial death" injury values. Thus we have credible estimates for the risk associated with exposure to ionising radiation, for instance, based on a reasonably well-founded linear or sigmoid model of impact against dose.

Interestingly (to me at least) this suggests that danger money is not illegal but actually written into law. The annual dose limit for an employee, i.e. someone whose income depends on occupational exposure, is 20 times that for a member of the public, and we can assign emergency levels up to 5 times that for a single exposure incurred in attempting to save life.

There is a significant difference between objective risk, on which we base engineering decisions, and perceived risk, that determines customer behavior. You could drive a tank and be reasonably certain of surviving any collision - even with another tank - but it would make a mess of the road, burn lots of fuel, and be limited to about  45 mph, so most folk drive something with a finite NCAP squashability rating rather than 30 tons of armor.

I dispute BC's suggestion that people "tolerate" car crashes but not plane crashes. Neither driving nor flying is banned (which would be the case if either were intolerable) but both are subject to regulation and the survivors complain like mad in the event of a collision. In an average year I fly about as far as I drive and find aviation far more tolerable (no traffic jams, no road works, no pedestrians, very few idiots changing lane without signalling) and studiously try to avoid crashing either vehicle.

Anyway, 1500 UK road deaths per year gives us an annual risk index (see reply #6 above)  R = 5.3, the level at which I suggested people expect some degree of statutory regulation, which we have. My index coincides pretty well with the will of Parliament and the attitudes of rational people.   

[evan_au]

people behave more carefully when they perceive more risk,

Apparently, after cyclones were given both male & female names (back in 1975), it was discovered that female-named cyclones killed more people than male-named cyclones. ("Cyclone" is Australian for hurricane.)
- I saw a speculation this week that female-named cyclones were perceived as less threatening than males, and so people took fewer precautions!
- Of course, if we went the next step and started giving cyclones names from multiple languages, that effect would disappear - and perhaps we may see racism in cyclone deaths? Names in languages that were perceived as more threatening might kill fewer people?

This came up in the context of heat waves - apparently Spain & Portugal have started naming heat waves
- It has been claimed that heat waves have killed more people in Australia than all other natural disasters combined (since modern records began)
- A week ago, I noticed the Bureau Of Meteorology* starting to quote "Dew Point" in weather reports. They said that with a dew point above 24C, some people will start to suffer heat stress (especially the elderly and the young). And that day had a dewpoint of 24C.

*The obvious (and common) nickname for the Australian Bureau Of Meteorology is "BOM" (pronounced "bomb"). Last year they came out with a press release stating that they were only to be called the Bureau Of Meteorology, and never "BOM"... Maybe people had realised that they were dropping too many climate bombshells, after they had to add an extra colour to the weather maps to denote extreme temperatures (purple is higher than red or black).

Australia_Heat_map.png (429.45 kB . 966x606 - viewed 1898 times)

http://www.bom.gov.au/australia/charts/viewer/index.shtml?type=T&level=2m&tz=AEDT&area=Au&model=CG&chartSubmit=Refresh+View

[alancalverd]

Looks very much like my favorite tourist map of Australia. There's a green strip round the edge marked "sharks, octopuses,  spiders, snakes and poisonous toads" and a red blob in the middle marked "nothing".

[Bored chemist]

I dispute BC's suggestion that people "tolerate" car crashes but not plane crashes. Neither driving nor flying is banned (which would be the case if either were intolerable)

They plainly tolerate car crashes so I presume you agree with me on that.
But the electorate has (indirectly) insisted on much more stringent regulations for aircraft safety- to the point where plane deaths are much rarer by most measures (maybe all).


So they are clearly less tolerant of plane crash deaths.
Which was the point.
And,  if you look at what I said "if you include the facts that people tolerate risks that are common but don't kill many (like car crashes), rather than risks that are rare but do kill a lot of people (like plan crashes)", you will see I was saying that they have a preference "They tolerate A rather than B".
I could have made it clearer but I figured the audience here was bright enough to understand. It looks like most were.

[Bored chemist]

Cars kill ~1500 Brits a year, I don't think that many are killed by planes, what's in operation is the Availability Heuristic: people perceive probability according to how easily something springs to mind.

I know more people who have been in car crashes than have been in plane  crashes.
So the "availability" argument isn't convincing.
If anything, it's the other way round. The newspapers etc publish stories about 10 people dying in a plane crash but not about the 25 killed on the road each month precisely because people are more interested in rare events involving a moderately large number than in the thing which kills a lot more people, but by a steady drip feed of corpses.

I'm told most drivers think they are "better than average" so they aren't so concerned about risks from their own driving.
(If I really wanted to cause an argument, I'd make the point that gun owners think that "their gun" keeps them safe, but "everybody else's gun" is a threat).

The big reason are less scared of car travel than plane travel is related to the perception of control.
People don't think they will crash their own car. Every year about 1500 find out (briefly) that they are wrong.

[evan_au]

Teaching logarithmic scales to children has been split off into a "New Maths?" topic under "New Theories":
https://www.thenakedscientists.com/forum/index.php?topic=86692.0
All comments are welcome!

[alancalverd]

They plainly tolerate car crashes so I presume you agree with me on that.

I have never met anyone (outside of a banger race track) who found a car crash tolerable. Most people try to avoid them, but acknowledge  their own and others' fallibility. Being a bit of a pedant, I can differentiate between tolerating something, like a smelly but friendly dog,  and acknowledging the inevitability of something wholly unpleasant, like death and taxes.

I'm not convinced that air travel is more stringently regulated than road transport. The standard passenger lap belt on a plane would not pass an MoT inspection.

[alancalverd]

(If I really wanted to cause an argument, I'd make the point that gun owners think that "their gun" keeps them safe, but "everybody else's gun" is a threat).

I recall a sensible American student being interviewed after what has become a routine classroom slaughter. Interviewer (Fox News) asked  why he didn't carry a gun for self-protection. He said "If the police turn up and see me holding a gun, they will shoot me."

[Petrochemicals]

I'm not convinced that air travel is more stringently regulated than road transport. The standard passenger lap belt on a plane would not pass an MoT inspection.

"In the event of a head on smash.............."