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June 14

Scientific Notation base

Does anyone have an opinion (or a factual argument) about whether the term "Scientific Notation" always implies base 10, or if it can be used with any base? Our article is somewhat ambiguous on the question. (I have started a thread on its talk page.) Stated another way, if I say "binary scientific notation", is that a fine way to refer to a representation of the form m × 2ⁿ, or a fine way although a pedant might complain, or a not-so-fine way, or a total howler? (To be on the safe side I can definitely say "binary exponential notation", but I'm still wondering about "scientific notation".) —scs (talk) 02:53, 14 June 2022 (UTC)[reply]

As the term "scientific notation" is commonly used, the base is always 10, as stated explicitly here. However, not everyone agrees.^[1] People who understand both scientific notation and binary notation will also understand what is meant by "binary scientific notation", and the term can be found used.^[2][3][4] There are also uses of "hexadecimal scientific notation" in the literature.^[5][6][7] --Lambiam 03:46, 14 June 2022 (UTC)[reply]

I searched in onelook.com for "scientific notation". Every dictionary where I found a definition indicated that it meant base 10. However, one of them—Merriam-Webster—includes a couple of example sentences collected automatically(!) from the Internet, and one of those is an article in Ars Technica by Jim Salter. Talking about the confusion based on describing amounts of storage in multiples of powers of 1024 or of 1000, he writes: "Filesystems almost universally use the powers of two (standard scientific notation), whereas storage device specifications are almost universally in powers of ten." So this sentence that M-W found to illustrate their definition does not actually conform to it. And in my opinion Salter was wrong to use those words that way and Steve is loony to ask his question. --174.95.83.56 (talk) 05:43, 14 June 2022 (UTC)[reply]

Doesn't the first sentence of the last section (Other bases) sum it up pretty well: "While base ten is normally used for scientific notation, powers of other bases can be used too". In other words ten is the default unless explicitly stated otherwise. Martin of Sheffield (talk) 08:13, 14 June 2022 (UTC)[reply]

Just an opinion: the answer is that a pedant might complain. I'm a pedant (in this question, and many others). If the analogy to scientific notation is important to you, I'd suggest calling it "generalized scientific notation" for bases other than ten.

(There is another class of pedant of the opinion that adding an adjective to a noun never extends the noun's meaning, but only restricts it. They're wrong, but it may be easier to cater to their preferences than to get into the seven millionth "a dwarf planet is a planet by definition!" argument). IpseCustos (talk) 08:30, 14 June 2022 (UTC)[reply]

Thanks, all — this is just the sort of reference information I was looking for. (My hunch about usage is basically confirmed — but I wanted something more than just my own hunch.) —sc "loony" s (talk) 11:38, 14 June 2022 (UTC)[reply]

If you represent a number as m×10^n with 10 being the binary representation of two and m and n also in binary, you have scientific notation in binary. But if you write m×2^n with m and n in decimal, you use a mixed system. My computer can also use a mixed system. When it says my file is 513kiB in size, 513 is decimal, but the ki prefix stands for 1024 and is part of a binary system. Imperial units also form a mixed system. PiusImpavidus (talk) 16:38, 14 June 2022 (UTC)[reply]

Good point. I tend to write m×2ⁿ where m is base 2 and n is base 10, which I guess is extra mixed. And then, in C, printf's %a format boils down to m×2ⁿ with m in base 16, which I find really annoying... —scs (talk) 17:52, 14 June 2022 (UTC)[reply]

Parkinson

Does Parkinson’s disease damage the ability to think and reason? --62.18.86.132 (talk) 21:27, 14 June 2022 (UTC)[reply]

Yes, Parkinson's disease#Neuropsychiatric mentions some cognitive challenges. Larry Hockett (Talk) 21:32, 14 June 2022 (UTC)[reply]

Path of moon

For any given point on earth, are there any parts of the sky that the Moon does not pass through at some time? When was this proven? Thanks. — Preceding unsigned comment added by 86.186.37.132 (talk) 21:48, 14 June 2022 (UTC)[reply]

The path of the Moon is near the ecliptic so there are definitely parts of the sky that it would not pass through. It stays within a band circling the Earth that is +/- 5 degrees from the ecliptic.[8] --mikeu ^talk 22:01, 14 June 2022 (UTC)[reply]

Thank you. Presumably this was fully known to all ancient civilisations and would have been written down at some early time in history. 86.186.37.132 (talk) 22:09, 14 June 2022 (UTC)[reply]

You are welcome. I assume so, but couldn't find a reference. I suspect that it was so obvious it was noticed before written history. --mikeu ^talk 22:14, 14 June 2022 (UTC)[reply]

Yes, so how long would one have to observe, to know that this was true? A year? 86.186.37.132 (talk) 22:21, 14 June 2022 (UTC)[reply]

It would only take months to notice but I would give it a year or so to confirm that there is a pattern that repeats. After that it becomes pretty obvious. --mikeu ^talk 22:37, 14 June 2022 (UTC)[reply]

Thank you. Of course, ancient civilisations had no concept of the earth or, therefore, the notion of "any given point on earth". So that must have come later. 86.186.37.132 (talk) 22:41, 14 June 2022 (UTC)[reply]

Ancient civilisations had words for Earth (𒅕𒍢𒁴, ארץ, γῆ) and a concept of "a point on Earth", which is meaningful regardless of whether your mental model is that of a flat Earth or a globe. For any given point on Earth, such as where some ancient stargazer may have had their domicile, the major part of the sky is Moon-free all year round. The Moon is never anywhere near the North Star. This cannot be "proven"; our best astronomical models, combined with our understanding of the laws of physics, can at best tell us not to expect the Moon venturing out of its orbit any time soon. --Lambiam 02:54, 15 June 2022 (UTC)[reply]

It's hard to figure what the IP meant by "of course", since it's demonstrably false. He might mean "earth as we now understand it", but that's true of lots of ancient concepts. --←Baseball Bugs ^{What's up, Doc?} carrots→ 04:43, 15 June 2022 (UTC)[reply]

You may be interested in Lunar distance (astronomy) in which people as early as 4th century BC observed that moon was in a different place in the sky when observed from different places on Earth. So they were able to work out how far away the Moon was at that time. Graeme Bartlett (talk) 05:21, 15 June 2022 (UTC)[reply]

Thank you, that's exactly what I was looking for. I agree "prove" is the wrong word. I meant that ancient people did not have astronomical knowledge from all over the earth as they never travelled that far or had the technology to gather it. 86.186.37.132 (talk) 07:28, 15 June 2022 (UTC)[reply]

You are actually talking about the Zodiac, that part of the sky which the Sun (and also the Moon) travels through. It appears to be of great antiquity, going back to at least Babylonian astronomy -- Verbarson ^talk_edits 08:58, 15 June 2022 (UTC)[reply]

You don't have to observe the Moon simultaneously from different places on Earth to get a distance. Just observe it from a single place over a few days and make use of the Earth's rotation and you can get a parallax measurement. You still need the radius of the Earth.

The Moon moves along the ecliptic, plus or minus 5 degrees as the orbital plane of the Moon isn't exactly aligned with the orbital plane of the Earth, plus or minus 1 degree due to parallax. PiusImpavidus (talk) 09:18, 16 June 2022 (UTC)[reply]

It's made more obvious by the fact that the sun, moon and naked-eye planets all move in a narrow band. Indeed, they're all lined up currently in the morning in their order from the sun (the moon joins them on the 24th). 2A00:23C5:C719:7201:1A:5EB9:69D5:D178 (talk) 16:58, 17 June 2022 (UTC)[reply]