Radiation

[nomuse]

That was my gut feeling....Tim was looking at a line around 2 and reading it as if it were 5.

[Jason Thompson]

So my point is, that the lines, that divide the units on the y-axis in the CRaTER "graph" (for short) in smaller increments, are not helpfull. They are meaningless and confusing as the y-axis is logarithmic. So why are they there?

As I tried to get Tim to understand, they are actually not there, at least not as increments on the y-axis. Unfortunately the decision to plot the gridlines as dotted lines has led to confusion. However, if you zoom into the axis you can see that what is actually happening is that the 'minor divisions' on the y-axis are actually just the dotted line from the first point on the x-axis. This is clear when you zoom in, as the major divisions on the y-axis don't align with these dots. Notably the 10⁰ point on the y-axis is between two of the dots. If you zoom in you just can't make the numbers work with those dots as minor divisions on any scale. There are just a few too many.

Attached below are the zoomed axis image I posted earlier and an altered version of the graph with the actual gridlines on it.

[Luke Pemberton]

That was my gut feeling....Tim was looking at a line around 2 and reading it as if it were 5.

That's exactly what he was doing, and getting 5 x 10^-2 cGy day^-1, or 0.5 mGr day^-1.

Even so, his wrangling over it being an arithmetic graph scaled exponentially was back pedalling of the highest order. When he introduced the idea of taking a log of the data before plotting the data against the log scale, I knew he didn't understand the graph.

I don't think it was obvious to him what the minor lines mean as we focused on trying to get him to understand how the major scales are spaced equally with an increasing order of magnitude. Did anyone, at any time, explain the way in which the minor scales are scaled; or was this futile given his fixation with the presentation of the CRaTER graph? After all, he seemed convinced that the dashed lines were scaling the y-axis linearly.

[theteacher]

So my point is, that the lines, that divide the units on the y-axis in the CRaTER "graph" (for short) in smaller increments, are not helpfull. They are meaningless and confusing as the y-axis is logarithmic. So why are they there?

As I tried to get Tim to understand, they are actually not there, at least not as increments on the y-axis.

You are correct and I apologize for not having paid adequate attention to what you wrote in the post you mention, although I remember the picture, which I never bothered to click. On the other hand it justifies, that my employer as of today has granted me free glasses for screen work 

[nomuse]

And that's just the start of it.

I mean, if you can't even read the graph properly, what's the point of going on from there?

(I still opine that if there's any question about interpreting the graph, then look at the numbers themselves.)

But still... once you get past the graph, you still have to deal with the problem that, as my friend put it, neither of us have a half mil in assets, despite what the median is for the US...the 1% throw those numbers off considerably. And the Crater data is both visibly and mathematically (the SD that Tim listed, err, copied himself) "spikey." One glance at the numbers tells you that it is a relatively low level of activity with short-lived spikes that drive the median up. It's hard to get a signal where the mean and the median are the same, so confuse them at your peril!

And then it is silly to sum up a year (well, particularly a non-representative year) for an activity that got to chose which part of the year. It's like saying you can't wear shorts in Paris because it snows there.

And then this is "radiation" arriving at detectors. A human astronaut is inside a spacecraft. Not only does a human have different quality factors for each potential ionizing threat, each is ameliorated differently. You can't just wave vaguely at bremsstrahlung and thus just add all your particles together, regardless of energies, to get one simplified picture.

But you know what's really funny? After all of that....he comes in within a power of two of what was actually recorded. His error bars are a magnitude above that. Some of us are happy enough with the results of a Fermi Estimation (his favorite song from an American musical? 100 trombones!)

When you do a napkin sketch and it is in the ballpark of the real-world numbers, you pat yourself on the back. You don't run to the highest steps and start shouting "NASA is wrong I just proved it!"

[Luke Pemberton]

And then this is "radiation" arriving at detectors. A human astronaut is inside a spacecraft. Not only does a human have different quality factors for each potential ionizing threat, each is ameliorated differently. You can't just wave vaguely at bremsstrahlung and thus just add all your particles together, regardless of energies, to get one simplified picture.

Ahhhh, glad you said that, as I was hoping we would begin discussing that with Tim next. I eluded to this point a few posts ago. I remarked to Ben that using the CRaTER data is dubious at the very least as it will give different readings to the Apollo dosimeters. Not only because the CRaTER detectors are naked in space as you elude to in you post (which is a version of the Muppet's, Pigs in Space), but they are different instruments so there will errors between instruments. That's the problem with measuring stuff, no two methods are the same. Science is a bit pesky like that.

But you know what's really funny? After all of that....he comes in within a power of two of what was actually recorded. His error bars are a magnitude above that. Some of us are happy enough with the results of a Fermi Estimation (his favorite song from an American musical? 100 trombones!)

The CRaTER data are ball park and in some instances well below the recorded Apollo doses, as Jason mentioned in a previous post. In fact I'm glad for the CRaTER data, as this puts to bed the ideas toted by a certain YouTube HB's, namely radiation levels beyond LEO are a raging furnace of death. Again, I'm glad you have drawn this conclusion about the error bars.

When you do a napkin sketch and it is in the ballpark of the real-world numbers, you pat yourself on the back. You don't run to the highest steps and start shouting "NASA is wrong I just proved it!"

I've had similar thought. The CRaTER data are not too dissimilar to the Apollo doses, a far cry from the raging furnace of death some HB's would lead one to believe.

OK, two things. Tim wants to use the CRaTER data to provide a threshold to judge whether NASA has taken part in skullduggery. He's going the wrong way as he will always compare apples with pears when trying to extrapolate data to the actual missions. Second thing, the CRaTER data shows nicely that the radiation outside of the VABs is survivable.

In one sense, Tim has done use a service as we can point to those naysayers that suggest the astronauts received 100s of rem per mission and highlight the CRaTER data dose not show that to be the case. Only in the event of an SPE do the levels spike. Which is precisely the message they have been given all these years.

[nomuse]

Hmph. Well, Tim ignored both the difference between "high" CREEP and "low" CREEP in his own sources, and the vast difference in activity between active and peaceful sun in mine.

But then, when we left off he was still thinking in terms of long-lived isotopes. Not of, if I understand correctly, a sort of nuclear spalling. Which might include a few isotopes along the way but with half-lives in the femto scale it hardly matters.

[smartcooky]

Would it be correct to say that the ten equally space minor divisions between 10⁰ and 10¹ would be 10ⁿ where n= a decimal fraction of 1

so

10⁰ = 1 (major division)
10^0.1 = 1.259
10^0.2 = 1.585
10^0.3 = 1.995
10^0.4 = 2.512
10^0.5 = 3.162
10^0.6 = 3.981
10^0.7 = 5.011
10^0.8 = 6.310
10^0.9 = 7.943
10¹ = 10 (major division)

[Luke Pemberton]

Would it be correct to say that the ten equally space minor divisions between 10⁰ and 10¹ would be 10ⁿ where n= a decimal fraction of 1

so

10⁰ = 1 (major division)
10^0.1 = 1.259
10^0.2 = 1.585
10^0.3 = 1.995
10^0.4 = 2.512
10^0.5 = 3.162
10^0.6 = 3.981
10^0.7 = 5.011
10^0.8 = 6.310
10^0.9 = 7.943
10¹ = 10 (major division)

If you are spacing the numbers on the left of your '=' sign equally in actual distance, then yes. But it makes no sense. Now try plotting data on that scale, because the numeric distance between minor scales is not equal. It would be utterly crackers to use that as a scale.

That's why the log scale has minor scales that become closer together, as the minor scale are derived from exponents of x in the function of 10^x (not exponential, that's something different), where x are mapped using a log function to represent equal increments between the major scale. The difference between successive values of x are not equal, but the difference between successive values of 10^x are equal.

So between 1 and 10 the first minor mark is 2, the next is 3, and so forth.

If you were to label 2 in exponent form it would be 10^{0.30102999566398119521373889472449}

3 would be 10^{0.47712125471966243729502790325512}.

This then translates to equal distances between the numbers represented by the minor scale. Does that make sense?

[Luke Pemberton]

Would it be correct to say that the ten equally space minor divisions between 10⁰ and 10¹ would be 10ⁿ where n= a decimal fraction of 1

so

10⁰ = 1 (major division)
10^0.1 = 1.259
10^0.2 = 1.585
10^0.3 = 1.995
10^0.4 = 2.512
10^0.5 = 3.162
10^0.6 = 3.981
10^0.7 = 5.011
10^0.8 = 6.310
10^0.9 = 7.943
10¹ = 10 (major division)

... and I think this hits the nail on the head with Tim. I actually now believe that if you had the number 3.162 in your data, he was saying that would take a log of this to obtain 0.5, and the plot 0.5 against 10^0.5

This only works if the data matches the numbers on the right of the '=' sign. What happen if you have 8.5?

Log 8.5 = 0.93.

As you can see, by trying to scale exponents arithmetically, so to speak, you can don't have the linear scale that Tim suggests. Yes, the exponents themselves are spaced arithmetically, but when one computes 10^x the data does not map linearly to the scale. The only way to scale a graph this way would be to have infinite minor scales so you ensure the scale is bespoke for the data set.

This is explains why he was using the term exponential arithmetic graph. He was saying the exponents are spaced arithmetically.

[nomuse]

If you are plotting by hand, then yeah...you need a grid a human can work with. If you are using software to plot, then it doesn't need to look at the index lines. It can put the data whatever number of pixels it wants.

In any case, nobody makes a graph that changes shape depending on the scale you look at it. I'd be tempted to say that's the basic nature of a graph; that it is fractal. As in, theoretically (if the plotted data were actually to that many significant figures) you could zoom in infinitely and the curve would still be the same.

If Tim tried to put a sine wave on his weird hybrid graph it would get all bumpy.

[Luke Pemberton]

If Tim tried to put a sine wave on his weird hybrid graph it would get all bumpy.

Ah, that's the word I was looking for. It's a hybrid.

The major scales are based on a log scale, the minor are based on spacing the exponents arithmetically. I mean wow!!

[Luke Pemberton]

In any case, nobody makes a graph that changes shape depending on the scale you look at it. I'd be tempted to say that's the basic nature of a graph; that it is fractal. As in, theoretically (if the plotted data were actually to that many significant figures) you could zoom in infinitely and the curve would still be the same.

My bold, but I was thinking along these lines. Every time you need to plot a point on Tim's hybrid, you'd need to take a log of the data and zoom in to find a point (ETA: minor scale) that was a solution to value_of_point = 10^x.

The only way to scale a graph this way would be to have infinite minor scales so you ensure the scale is bespoke for the data set.

[Luke Pemberton]

This is what working with an exponential arithmetic scale using log data would be like.

[bknight]

This is what working with an exponential arithmetic scale using log data would be like.

Now that is kool. 😀