A common story - a guy is being wrong on the Internet.
In this case, the guy is dividing one number into another and then truncating (?) the results. The ‘ratio’ of the two numbers is reported to the first couple of leading digits. So:
384,000/3474.1 = 110.5322417 but gets reported as 1.105
149598023/12735 = 11,746.998 but gets reported as 1.17
998.5/232.55 = 4.29370 but gets reported as 4.3
Aside from the seemingly arbitrary number of significant digits, how is what this guy is doing described mathematically? Is ‘truncating’ the correct term? Wouldn’t “real” truncating be more like:
110.532 → 110
11,746.998 → 11000? or 11? I dunno.
4.29370 → 4.2
It’s called rounding. For example, Pi is a number with an apparently infinite number of digits after the decimal point, but most of us only need two or three, so 3.1415926535 is rounded to either 3.14 or 3.142. If you need more precision, you could keep going and use 3.1416 or 3.14159 - ∞.
Digits 1 to 4 are rounded down, while 5 to 9 are rounded up.
I would guess the OP know what rounding is, but look closely at the results. The number of significant digits it gets rounded to seems arbitrary. Also, the rounded answer from the first two results is orders of magnitude off what an actual rounded answer would be (unless that is an error by the OP putting the decimal in the wrong place.)
It seems like some kind of weird scaling or normalization, but I can’t make a lick of sense as to the rules behind it if those are actual and correctly written examples.
'Zactly. The issue here is not rounding or truncation of excess figures. Although they are doing either rounding or truncation along the way to their real mistake: moving the decimal place with zero mathematical basis.
Now this may just be a dumb formatting error, perhaps contributed somewhere along the chain by a computer, not a human.
But 110.5 is the same value as 1.105E2 or 1.105x10^2 or 1.105x102. These latter forms are commonly called “scientific” or “exponential” notation.
If this is the usual internet “most people get this wrong” stumper quiz, it’s probably passed through several authors being copied from place to place with ever-decreasing fidelity. I could sure imagine some plagiarist who wasn’t familiar with scientific notation simply leaving off everything except the familiar “1.105” part of the number as they gleefully upload someone else’s work to their site in pursuit of those schweet schweet clicks.
Yeah, it isn’t rounding. 11,746 doesn’t round to 1.17. The examples are copied correctly, directly from the source.
If it was straight truncating, I’m not certain whether 11,746 would be truncated as 11,000 or 117, but it probably wouldn’t be truncated as 1.17.
It is some kind of scaling or normalization, for large values of ‘some kind’.
The context is that this guy has an idée fixe about ‘round’ numbers (integer multiples of powers of 10), vs. ‘unround’ numbers that are midway between the ‘rounds’. So 40 and 50 are round, but 45 is ‘maximally unround’. Ditto 400 and 500 vs 450. Ditto 4000 and 5000 vs 4500. At the risk of getting too far into the weeds, he feels that the scaled (or truncated, or scaled and truncated, or whatever) ‘ratios’ of supposedly unrelated physical values fall closer to round numbers than would be expected by chance. I’m loath to give specific examples, because they’re dumb. It’s numerological and he seems to pick specific values that produce the ‘ratios’ that he likes to see. That’s why I didn’t flesh that out in the OP.
However, I did see a hint of two things of interest - first, significant digits aside, is this kind of leading-digit scaling or truncation a known practice? It’s kind of a bastard of logarithms and rounding or truncation somehow. Or maybe it’s just like madness like only writing down the last two letters of ry rd.
The second thing was a little more intriguing - if the numbers that he’s starting with follow Benford’s Law because they cross multiple orders of magnitude and he scales or truncates his answers in this way, then might there not be a tendency for the ‘ratio’ results to be very small and close to integer values?
It seems from the responses so far that the sort of ‘normalizing’ that he’s doing is just number magic, though.
Are the first two the ratio of the distance to the moon and the moon’s diameter and the second the same with the sun and earth? Can’t figure out what the third is, tho.
I mean, if that’s the hypothesis that he’s testing, then taking the first few digits (without regard to where the decimal point is) would be a valid procedure… but it’s certainly a weird hypothesis.
You could phrase what he’s doing in terms of the mantissa, I think.
If he was including a “times10^x” then it would be scientific notation and it is common practice, probably related to Fermi problems, where you’re sort of accepting that you’re just eyeballing it and the more important thing is the number of digits, not what the digits actually are.
Without the exponent, though, it’s just being a crazy person. And your description of his thinking would seem to confirm that.
I’ll confess that I cheated and asked Chat GPT to see if there’s any significance to those numbers, because I assumed there was something there and it would have otherwise taken me a little while to figure out the link.
Yeah, I’ve got no illusions about changing this guy’s mind about his discovery. I was more intrigued by the possibility that Benford’s Law was maybe involved, since almost all of the values that he’s comparing start with 1, 2, or 3; so when he divides ~1,300,000 by 12,735 and calls the answer 1.09, of course it’s going to be close to 1.
No, the dude is explicitly truncating things this way. At the risk of summoning the TimeCube, some paraphrases:
‘(in calculating ‘ratios’), we … reduce the result to a single decimal place.
For example, if we move the decimal point of the number 400.5 two
places to the left, the resulting number is 4.005, which falls between
3.5 and 4.5, within the range of 4.’
‘distance to sun/size of earth = 11,747 -->1.17’ 'speed of light/rotation of Sun = 300,243 -->3.00
I guess you could say he’s normalizing all his ratios to the interval [1,10)?
Looking at just the mantissa, is it possible that arbitrary numbers will generally have a mantissa that is closer to 1.0 than to 9.9? Could this person just be reformulating Benford’s law using strange tools?
The one place where this might be useful is studying Benford’s law. Now if this guy is a crank, as seems likely, he may also being trying to abuse Bedford’s law to make a point. “Isn’t it amazing how most of the numbers I end up with tend to be between 1 and 2, while very few are between 8 and 9. Therefore there must be some grand creator.”
Truncation usually means taking away less significant digits to the right of the decimal, to some predefined degree, but that’s not what’s happening here.
This is a destructive operation that loses critical information along the way. The ratios 1.17 to 1 and 11700 to 1 are very different and “normalizing” them like this is going to destroy the original data’s integrity unless you are specifically looking for patterns in the first digit. And yeah, it’s going to look very different in other number bases.
Could it just be some good old fashioned trolling for attention? You can run any two numbers through some arbitrary algorithm and make a post about it, but it doesn’t have to mean anything at all…
