Well, for one the expression doesn't tell us anything, could as well describe alien gravity -- even if we know math. You still need to explain what S, M, and E are used for to understand it.
The only term there you might not remember from high school math is mantissa, and a search engine will precisely explain that in two sentences, in terms you do remember from high school math.
That doesn't actually get you any closer to knowing what the formula means, though. You need to also define that M is unsigned & 23 bits and E is unsigned & 8 bits. And that alone still doesn't get across the resulting limitations like that precision reduces by half every time the exponent bumps. Sure you can reason about it if you devote the brainpower to applying the limitations to the formula, but it's not explained by the formula itself.
edit: jordigh, not coldtea, first brought up the formula in his argument
That's generally considered a plus (if not a sine qua non) for a simplified explanation, and the larger the specification, the bigger plus.
Else, one might as well read the 100s of pages of specs.
"it is an abuse of terminology to call the fraction part a mantissa, since this concept has quite a different meaning in connection with logarithms"[1] –DEK
[1] https://en.wikipedia.org/wiki/Significand#Use_of_.22mantissa...
This isn't to say that visualizations aren't useful, of course.
Who said anything about strings?
>Nobody can look at a random graph and know what it stands for either.
Well, the parent wrote: "is (-1)^S 1.M 2^(E-127) so bad that it required a whole blog post to explain it?".
And the answer is, yes it is.
We can look at y = 2*x + 5 and understand it immediately. Sums, limits, and lots of other equations too.
Floating point though is an encoding/representation scheme, so it needs more than the mere equation to be understood. I don't just want to know I replace three numbers and do a calculation, I need to know what these numbers are supposed to represent.
What I don't understand is what's supposed to be uniquely puzzling about strings. Maybe I'm under the influence of the submission, because the guy said he had an allergy for notation. But even after putting a floating point expression in analogy with some geometrical constructs, the whole thing could still be a model of alien gravity, because neither the expression nor the geometric figures carry any inherent meaning in themselves. The only reason why we know that it is in fact just a pure representation of how to approximate real numbers is because the post itself tells us so.
I think you're trying to say that unlabeled formulas are no better or worse than unlabeled graphs and the like, but calling a formula a “string” is muddling it up. (If that is what you meant.) Because we're talking about floating-point data types, people are likely to think of the string data type.