Difference between revisions of "Talk:2566: Decorative Constants"
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:::Great thanks have included both references in the explanation. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 08:32, 11 January 2022 (UTC) | :::Great thanks have included both references in the explanation. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 08:32, 11 January 2022 (UTC) | ||
:Wait, wouldn't the values be twice as big (rather than half as big) if you left off the 1/2? [[Special:Contributions/141.101.69.154|141.101.69.154]] 12:43, 11 January 2022 (UTC) | :Wait, wouldn't the values be twice as big (rather than half as big) if you left off the 1/2? [[Special:Contributions/141.101.69.154|141.101.69.154]] 12:43, 11 January 2022 (UTC) | ||
| + | ::No. If 1/2Cd = Constant, then the new constant would be half as big as Cd since Cd=2x constant. You would just put in the 1/2 in the new version of Cd, so the new Cd is half as big as the old, and the final result the same.--[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:44, 12 January 2022 (UTC) | ||
Of course, the c^2 im e=mc^2 is just as decorative, when using natural units where c=1.... [[Special:Contributions/172.68.50.171|172.68.50.171]] 00:29, 11 January 2022 (UTC) | Of course, the c^2 im e=mc^2 is just as decorative, when using natural units where c=1.... [[Special:Contributions/172.68.50.171|172.68.50.171]] 00:29, 11 January 2022 (UTC) | ||
: And the resulting equation is then just e=m - or m=e which is beautiful and profound. "Mass is Energy". Without the complications, you stop thinking of it as a PROCESS for converting one into the other and get the more profound point that Mass and Energy are the exact same thing. [[User:SteveBaker|SteveBaker]] ([[User talk:SteveBaker|talk]]) 03:33, 11 January 2022 (UTC) | : And the resulting equation is then just e=m - or m=e which is beautiful and profound. "Mass is Energy". Without the complications, you stop thinking of it as a PROCESS for converting one into the other and get the more profound point that Mass and Energy are the exact same thing. [[User:SteveBaker|SteveBaker]] ([[User talk:SteveBaker|talk]]) 03:33, 11 January 2022 (UTC) | ||
| + | : I respectfully disagree. The c² isn't decorative; mc² is a measure of energy and m is not. e=mc², like f=ma, still works even if you change the size of any of the basic units (of length, time, mass) from which the units of energy and force are derived. As I see it, an equation that ties you to any definition of unit size is less profound, not more. [[User:Tom239|Tom239]] ([[User talk:Tom239|talk]]) 17:21, 12 January 2022 (UTC) | ||
| + | :: To the sort of person who (thoughtfully) uses c=1, this feels a bit like saying that the "f" is profound in dist=sqrt[x^2+y^2+(z/f)^2], where of course I've measured xy-distances in miles and z-distances in feet, so f=5280ft/mi. Yes, it's entirely possible to choose different units for different coordinates, and if you're very accustomed to that then the conversion factors can be deeply important for your understanding of the system (and provide extra flexibility in your choice of units: you can easily use "f=1760yd/mi" if you'd prefer). But there's still a very well-defined sense in which sqrt[x^2+y^2+z^2] is the more fundamental equation, and the "f" is an unnecessary complication (however convenient it may be). Whether I'd call it "decorative"... I'm not sure. But I don't see this "f" as profound. [[User:Steuard|Steuard]] ([[User talk:Steuard|talk]]) 17:59, 29 May 2022 (UTC) | ||
| − | + | I think the 1/2 in the drag equation is intuitive. I understand that it is technically superfluous, but F=Pd*A and Pd=1/2*rho*u^2 so the 1/2 carries over intuitively. {{unsigned ip|172.70.98.15}} | |
| − | + | :Agrees I had this written down in an early version of the explanation but that was edited out. Maybe I will put it in again.--[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:44, 12 January 2022 (UTC) | |
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| − | + | Drag coefficients could just as easily be half as big. This is true but how is their being unitless relevant? It's more about how defining constants is partially arbitrary. [[User:Lev|Lev]] ([[User talk:Lev|talk]]) 08:07, 12 January 2022 (UTC) | |
| − | + | :If Cd had a unit, say it was an energy which represented some relevant value for a given material, then it would not be correct to say that it was half as much, just because 1/2 came into the equation. But if it has no units, then it is just a constant saying something about the material, and then the 1/2 could in principle be absorbed without changing anything. But as stated above 1/2 actually has physical meaning in the way it enters the equation. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:44, 12 January 2022 (UTC) | |
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| − | : | + | :It doesn't make any difference. For instance, Coulomb's law works fine whether we write it F = -q<sub>1</sub>q<sub>2</sub>/(4πε<sub>0</sub>r<sup>2</sup>) or F = -kq<sub>1</sub>q<sub>2</sub>/r<sup>2</sup>. Similarly, if we had a factor of 2 in the gas law for some reason, that would just change the values of the gas constants. |
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| − | + | I've seen the double-struck capital "D" used commonly as a symbol for the Domain of a function (While the double-struck "R" was used for the range in that context) [[Special:Contributions/162.158.63.243|162.158.63.243]] 21:16, 17 January 2022 (UTC) | |
| − | + | :Any use of double-struck or bold capital R to mean something besides the set of real numbers can be considered nonstandard, like using + to represent a non-commutative function or using a fraktur lowercase c to represent anything other than the cardinality of the continuum. It happens of course, but it's not any kind of standard. [[User:EebstertheGreat|EebstertheGreat]] ([[User talk:EebstertheGreat|talk]]) 03:18, 20 August 2023 (UTC) | |
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| − | + | Does anybody know enough math to figure out what that equation is supposed to do? I really want to delete that tag.[[User:New editor|New editor]] ([[User talk:New editor|talk]]) 19:13, 25 January 2022 (UTC) | |
| − | + | :The r terms are used in describing things like water treatment plants or dialysis machines, where you're trying to use fluid flow to regulate some solute. If fluid balance is large, it means the "tank" is going to empty or dry out. I guess T is the rate at which this happens. Not really a math thing, more of an engineering thing, seems to me. | |
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| − | + | ==Count down clock== | |
| − | + | See [[Countdown in header text]]. Discussion has been moved here [[Talk:Countdown_in_header_text]]. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 11:10, 12 January 2022 (UTC) | |
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Latest revision as of 03:18, 20 August 2023
I don't have any idea what to put in the actual description, but whoever does should probably note that r(in) - r(out) equals zero, not one. And multiplying by a constant 0 absolutely changes the value! GreatWyrmGold (talk) 21:59, 10 January 2022 (UTC)
- rout and rin are different values. The subscripts represent different instances of the same variable at different point. In the same way, you might calculate something happening over a time interval tend - tstart . 172.69.71.77 23:02, 10 January 2022 (UTC)
- Yes for sure they are two different values. On the other hand if μ is not 1 then the it is not just decorative! D on the other hand is just a proportionality constant, which may have a value other than 1. I have tried to put something in the explanation here. Quite a bit. Do not really now anything about Drag, so just took it from the wiki page. Also I hope someone can explain the formula in the image, as I'm sure it is just something about the flow, that would relate it to a drag equation. --Kynde (talk) 23:41, 10 January 2022 (UTC)
Note that the title text is pretty much word-for-word a repeat from Randall's book *How To*. In Chapter 11: *How to Play Football*, he misuses the drag equation, and mentions this fact in more depth, in a footnote. Bit of trivia! --162.158.134.79 23:13, 10 January 2022 (UTC)
- Nice, I will have to check up on that. Thanks. --Kynde (talk) 23:41, 10 January 2022 (UTC)
- Can confirm this, the book mentions that the "traditional tribute to Euler and Bernoulli" comes from Frank White's Fluid Mechanics textbook. Clam (talk) 01:08, 11 January 2022 (UTC)
- There it is, page 266 in the 1986 2nd edition: "They both have a factor ½ as a traditional tribute to Bernoulli and Euler, and both are based on the projected area..." https://books.google.com/books?id=wGweAQAAIAAJ&q=traditional -- 172.70.162.5 02:13, 11 January 2022 (UTC)
- Wait, wouldn't the values be twice as big (rather than half as big) if you left off the 1/2? 141.101.69.154 12:43, 11 January 2022 (UTC)
Of course, the c^2 im e=mc^2 is just as decorative, when using natural units where c=1.... 172.68.50.171 00:29, 11 January 2022 (UTC)
- And the resulting equation is then just e=m - or m=e which is beautiful and profound. "Mass is Energy". Without the complications, you stop thinking of it as a PROCESS for converting one into the other and get the more profound point that Mass and Energy are the exact same thing. SteveBaker (talk) 03:33, 11 January 2022 (UTC)
- I respectfully disagree. The c² isn't decorative; mc² is a measure of energy and m is not. e=mc², like f=ma, still works even if you change the size of any of the basic units (of length, time, mass) from which the units of energy and force are derived. As I see it, an equation that ties you to any definition of unit size is less profound, not more. Tom239 (talk) 17:21, 12 January 2022 (UTC)
- To the sort of person who (thoughtfully) uses c=1, this feels a bit like saying that the "f" is profound in dist=sqrt[x^2+y^2+(z/f)^2], where of course I've measured xy-distances in miles and z-distances in feet, so f=5280ft/mi. Yes, it's entirely possible to choose different units for different coordinates, and if you're very accustomed to that then the conversion factors can be deeply important for your understanding of the system (and provide extra flexibility in your choice of units: you can easily use "f=1760yd/mi" if you'd prefer). But there's still a very well-defined sense in which sqrt[x^2+y^2+z^2] is the more fundamental equation, and the "f" is an unnecessary complication (however convenient it may be). Whether I'd call it "decorative"... I'm not sure. But I don't see this "f" as profound. Steuard (talk) 17:59, 29 May 2022 (UTC)
I think the 1/2 in the drag equation is intuitive. I understand that it is technically superfluous, but F=Pd*A and Pd=1/2*rho*u^2 so the 1/2 carries over intuitively. 172.70.98.15 (talk) (please sign your comments with ~~~~)
- Agrees I had this written down in an early version of the explanation but that was edited out. Maybe I will put it in again.--Kynde (talk) 10:44, 12 January 2022 (UTC)
Drag coefficients could just as easily be half as big. This is true but how is their being unitless relevant? It's more about how defining constants is partially arbitrary. Lev (talk) 08:07, 12 January 2022 (UTC)
- If Cd had a unit, say it was an energy which represented some relevant value for a given material, then it would not be correct to say that it was half as much, just because 1/2 came into the equation. But if it has no units, then it is just a constant saying something about the material, and then the 1/2 could in principle be absorbed without changing anything. But as stated above 1/2 actually has physical meaning in the way it enters the equation. --Kynde (talk) 10:44, 12 January 2022 (UTC)
- It doesn't make any difference. For instance, Coulomb's law works fine whether we write it F = -q1q2/(4πε0r2) or F = -kq1q2/r2. Similarly, if we had a factor of 2 in the gas law for some reason, that would just change the values of the gas constants.
I've seen the double-struck capital "D" used commonly as a symbol for the Domain of a function (While the double-struck "R" was used for the range in that context) 162.158.63.243 21:16, 17 January 2022 (UTC)
- Any use of double-struck or bold capital R to mean something besides the set of real numbers can be considered nonstandard, like using + to represent a non-commutative function or using a fraktur lowercase c to represent anything other than the cardinality of the continuum. It happens of course, but it's not any kind of standard. EebstertheGreat (talk) 03:18, 20 August 2023 (UTC)
Does anybody know enough math to figure out what that equation is supposed to do? I really want to delete that tag.New editor (talk) 19:13, 25 January 2022 (UTC)
- The r terms are used in describing things like water treatment plants or dialysis machines, where you're trying to use fluid flow to regulate some solute. If fluid balance is large, it means the "tank" is going to empty or dry out. I guess T is the rate at which this happens. Not really a math thing, more of an engineering thing, seems to me.
Count down clock[edit]
See Countdown in header text. Discussion has been moved here Talk:Countdown_in_header_text. --Kynde (talk) 11:10, 12 January 2022 (UTC)
