Please Show Lots of Digits(dynomight.net)
dynomight.net
Please Show Lots of Digits
https://dynomight.net/digits/
17 comments
I kind of like where you're going with that, it can be frustrating when we use worse notation due to historical accidents (see also, perhaps: direction of conventional current flow, pi vs tau, all the bad differentiation syntaxes).
Also, thinking in terms of log quantities makes me think of Fermi estimation, which I love.
But dropping units seems mad to me! From the page:
But then I'm a proponent that people should use WAY MORE units every day. Almost every number should have a unit after it. If I'm estimating how many people live on a street it should always be: "10 [houses] x 2.5 [people/house]" not "10 x 2.5".
Also, thinking in terms of log quantities makes me think of Fermi estimation, which I love.
But dropping units seems mad to me! From the page:
For instance, “10 million kWh” becomes “↑13.6”
But then I'm a proponent that people should use WAY MORE units every day. Almost every number should have a unit after it. If I'm estimating how many people live on a street it should always be: "10 [houses] x 2.5 [people/house]" not "10 x 2.5".
Oops! That was an error of manual conversion. The actual plugin converts it to "↑13.6 joules". Thanks for spotting, fixed it!
Outside of science people invent random units, they just say three football fields or 70 school busses. Which works just fine, aside from taking effort to write and maybe making some readers feel insulted.
Anytime you actually need to do anything with a number, you usually need more precision, and any new notation breaks the ability to copy and paste to a calculator, until all the calculators get support.
Anytime you actually need to do anything with a number, you usually need more precision, and any new notation breaks the ability to copy and paste to a calculator, until all the calculators get support.
Yes, that's currently what people do (including journalists and science explainers), and it does not work just fine. In fact it's kind of unbelievable that an intelligent and educated person would defend "inventing random units" as an acceptable tactic. I mean even just from your example, which is bigger, 3 football fields or 70 school buses?
And actually, anytime I need to do anything with a number, I either use a computer (in which case I'm not entering in the numbers manually), or I don't need more precision. In fact more precision completely gets in the way.
Also, we have an existing "scientific notation", which is completely incapable of being copy-pasted into any calculator I've ever used.
And actually, anytime I need to do anything with a number, I either use a computer (in which case I'm not entering in the numbers manually), or I don't need more precision. In fact more precision completely gets in the way.
Also, we have an existing "scientific notation", which is completely incapable of being copy-pasted into any calculator I've ever used.
I have no idea which one is actually bigger, even if I did know whether a school bus is a unit of weight or length or people or money...
But it works fine for the intended audience and purpose, which is usually to give a very vague idea without assuming any specialized knowledge. If they wanted to enable real reasoning with the data(which they probably should) then they could just give the actual number, in full precision.
I would imagine a lot of this is just an individual thing. Some people make real decisions with mental arithmetic on a regular basis, others almost never encounter math outside of a screen, because apps have taken over a lot of the stuff that used to be done mentally.
But it works fine for the intended audience and purpose, which is usually to give a very vague idea without assuming any specialized knowledge. If they wanted to enable real reasoning with the data(which they probably should) then they could just give the actual number, in full precision.
I would imagine a lot of this is just an individual thing. Some people make real decisions with mental arithmetic on a regular basis, others almost never encounter math outside of a screen, because apps have taken over a lot of the stuff that used to be done mentally.
>Outside of science people invent random units, they just say three football fields or 70 school busses. Which works just fine, aside from taking effort to write and maybe making some readers feel insulted.
Is this something people do? I only saw this in English (American I guess) online articles.
Is this something people do? I only saw this in English (American I guess) online articles.
Notation is in the data repository. Exposition is for understanding.
I like your Mag World initiative. I had a similar idea… we should reform / simplify how units are dealt with
Wouldn’t the proper solution to this be to fix how data is published? Instead of making the actual paper unreadable to help people replicate it, maybe require a standardized structure to provide the necessary data and code to replicate the calculations?
In my studies we had to underline the significants digits
This seems to be written by someone who has no idea of what they are talking about. Propagation of significant digits over algebraic operations is a solved problem. Adding more digits than the minimum necessary significant digits does not get you anything extra. Literally the first class in Physics 101 courses teaches this.
Your comment seems to be written by somebody who has no idea what they are talking about. (Meaning, the contents of the article they supposedly just read.)
Once you bother to get past the first paragraph, the entire rest of the article explains exactly why the extra digits are useful to the author in some specific circumstances. (Hint: it has exactly nothing whatsoever to do with propagation of significant digits, which they also clearly demonstrate their understanding of.)
Once you bother to get past the first paragraph, the entire rest of the article explains exactly why the extra digits are useful to the author in some specific circumstances. (Hint: it has exactly nothing whatsoever to do with propagation of significant digits, which they also clearly demonstrate their understanding of.)
This has everything to do with propagation of significant digits.
Since the data in the mentioned experiment are "exact" measurements without uncertainty, the data is being treated as infinite (or rather, machine) precision, where the percentage difference would also have to be reported at machine precision, which is what the author is getting at:
>>> 100 * ((37/45) / (312/401) - 1)
5.676638176638171
However, assume that the same kind of data came from a sensor with some uncertainty (say, 2 digits precision), then you could have, within that uncertainty bound, L = 46 (instead of L = 45, etc.), R = 400 (and still L+R = 446), which would give
>>> 100 * ((37/46) / (312/400) - 1)
3.121516164994431
Obviously, this is a huge difference, which is why propagation of significant digits needs to be considered if there is any uncertainty in the data. And in that case adding more digits will not buy you anything.
The author's case is a special case where the values are "exact" and therefore you need more precision in the reported percentage value. But it is often not applicable in science when measured data has uncertainty.
Since the data in the mentioned experiment are "exact" measurements without uncertainty, the data is being treated as infinite (or rather, machine) precision, where the percentage difference would also have to be reported at machine precision, which is what the author is getting at:
>>> 100 * ((37/45) / (312/401) - 1)
5.676638176638171
However, assume that the same kind of data came from a sensor with some uncertainty (say, 2 digits precision), then you could have, within that uncertainty bound, L = 46 (instead of L = 45, etc.), R = 400 (and still L+R = 446), which would give
>>> 100 * ((37/46) / (312/400) - 1)
3.121516164994431
Obviously, this is a huge difference, which is why propagation of significant digits needs to be considered if there is any uncertainty in the data. And in that case adding more digits will not buy you anything.
The author's case is a special case where the values are "exact" and therefore you need more precision in the reported percentage value. But it is often not applicable in science when measured data has uncertainty.
The ratios in the example are on integer numbers of people, not measurements. You seem to get that, so I'm struggling to imagine what "the same kind of data" from a "sensor with some uncertainty" would even mean. Or what the hypothetical experimentalist who wrote your modified version of the equation would even be trying to compute using the measurements, in that case. Or why any reader would be attempting to "reverse engineer" the experimental details in a case like that. It just flat out doesn't apply to the situations the author is writing about. If I'm not getting your point, feel free to paint me a scenario with a bit more specificity.
Anyway, if you're worried about not tracking uncertainty in calculations, well, I can quote from the article:
> If your point is that there’s lots of uncertainty, then add a confidence interval or write “±” whatever.
That solves the problem in an equally valid way, no? The author is clearly not some ignoramus who doesn't understand significant digits and needs to take a Physics 101 class.
Anyway, if you're worried about not tracking uncertainty in calculations, well, I can quote from the article:
> If your point is that there’s lots of uncertainty, then add a confidence interval or write “±” whatever.
That solves the problem in an equally valid way, no? The author is clearly not some ignoramus who doesn't understand significant digits and needs to take a Physics 101 class.
I won't argue against this specific case. But in almost any other context, I think comprehension would be better served with zero significant digits, or at most 1. This is one reason that I propose magnitude notation: https://saul.pw/mag.