- #36
olgerm
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Roman numerals are not mathematically more beautiful than postional-notation of numbers (especially on base 2). Mathematical beauty is different from what you call beauty here.
Replacing the Measurement standards (SI units)
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- #37
bob012345
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Not necessarily. Perhaps the Pythagoreans would relish a more complex system only they understood.
- #38
olgerm
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You still do not understand meaning of mathematical beauty. Even if someone would enjoy mathematically less beautiful notation more, it would not make this notation mathematically more beautiful.
- #39
weirdoguy
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You are a perfect example: you enjoy using ##*## instead of ##\cdot## for denoting multiplication, even though it hurts eyes of most of the people who reads that.
- #40
bob012345
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You obviously have a strong opinion and perhaps most people might agree with it. I understand it but I believe mathematical beauty is in the eye of the mathematician or the physicist if we are talking about expressions of physical theories such as QED which I have heard described as the most beautiful theory . To quote Wikipedia:
Mathematical beauty is the aesthetic pleasure typically derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians often express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. They might also describe mathematics as an art form (e.g., a position taken by G. H. Hardy[1]) or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
According to this definition, if someone enjoyed a mathematically less beautiful notation (according to some) more, it would make this notation mathematically more beautiful to them. I think the whole concept of mathematical beauty is fraught with subjective values and it is not about telling others what is or is not beautiful. This is not about a majority opinion.
- #41
bob012345
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- #42
N1206
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I think you haven't thought your thought through.
Napoleon wanted a new system of measurement, and he had one created and imposed it on much of Europe and it stuck. The French Revolutionaries tried to get rid of the old calendar and systems of time. That did NOT stick. Units of measurement are USED by people--and they have habits. And old habits can be VERY hard to break. QWERTY, for example, was good for typewriters that had actuated swinging arms. Are you still using a QWERTY keyboard? You almost certainly are!
Old standards are sticky. Most of North America is gridded out in blocks measured in miles. Kilometers have made some inroads, but directions on the grid of roads laid out in miles still usually get related in miles. Ask anyone in North America for their height and weight. You will invariably get feet, inches and pounds in the reply. Land is in acres. Houses are in sq. ft. Recipes are usually still in pounds, ounces, tbsp and tsp, and NOT in grams and milliliters. Pressures are in psi and not Pa, or kg/cm2. Mechanical stuff has a mix. If it comes from abroad, you may need metric tools--or SAE tools--and you have both because you just never know. Bulk fuel in Canada get measured in litres--mainly because the imperial gallon was a unit ONLY Canadians were using, and so letting that go was easier.
Units get USED. Energy is nominally measured in joules. But your electric bill comes as kilowatt-hours and physicists like electron-volts. While physics and engineering are SUPPOSED to be in SI units, you do wind up with CGS or MKS depending on the scale of what you are doing (centimeters, grams, seconds vs metres, kilograms, seconds. If existing units are not convenient, rest assured that someone will create some SI-based one that are. You'll see some hard SF (Larry Niven and Arthur C. Clarke in particular) where a spaceship's propellant mass and energy are given as delta-v with units given as c (the ship was carrying 2.5c of delta-v, meaning it could alter its velocity a total of 2.5 times the speed of light accelerating and decelerating before running out of maneuvering ability.) We talk about fuel range in miles or km for cars -- but in minutes for aircraft. Units depend on usage. (part of why Bitcoin will never be a thing is that nothing will EVER be priced in bitcoin, it is not a convenient unit of account, nor will it ever be a stable one.) There will NEVER be one universal system of units to rule them all.
And then really, almost nothing is constant. Supposedly the distance between two stationary objects is a function of the age of the universe. The passage of time is influenced by the velocity at which you are travelling. Mass too is a function of velocity (the mass of the proton involved in a cosmic ray can be several kilograms viewed in a particular frame of reference.) Distance too is a function of velocity ( at v approaching c distances measured perpendicular to the direction of travel are not the same as those measured parallel to it.) g changes as you move away from the center of the earth. And on it goes. and on, and on.
Reality does have some constant, unitless numbers embedded in it, but they generally don't lend themselves to the construction of systems of units that are convenient to use. We do try to count where we can, rather than bulk (Avogadro's number) But nobody is purchasing bread flour in mols. So, I don't think trying to replace SI units is an exercise in anything but futility.
Napoleon wanted a new system of measurement, and he had one created and imposed it on much of Europe and it stuck. The French Revolutionaries tried to get rid of the old calendar and systems of time. That did NOT stick. Units of measurement are USED by people--and they have habits. And old habits can be VERY hard to break. QWERTY, for example, was good for typewriters that had actuated swinging arms. Are you still using a QWERTY keyboard? You almost certainly are!
Old standards are sticky. Most of North America is gridded out in blocks measured in miles. Kilometers have made some inroads, but directions on the grid of roads laid out in miles still usually get related in miles. Ask anyone in North America for their height and weight. You will invariably get feet, inches and pounds in the reply. Land is in acres. Houses are in sq. ft. Recipes are usually still in pounds, ounces, tbsp and tsp, and NOT in grams and milliliters. Pressures are in psi and not Pa, or kg/cm2. Mechanical stuff has a mix. If it comes from abroad, you may need metric tools--or SAE tools--and you have both because you just never know. Bulk fuel in Canada get measured in litres--mainly because the imperial gallon was a unit ONLY Canadians were using, and so letting that go was easier.
Units get USED. Energy is nominally measured in joules. But your electric bill comes as kilowatt-hours and physicists like electron-volts. While physics and engineering are SUPPOSED to be in SI units, you do wind up with CGS or MKS depending on the scale of what you are doing (centimeters, grams, seconds vs metres, kilograms, seconds. If existing units are not convenient, rest assured that someone will create some SI-based one that are. You'll see some hard SF (Larry Niven and Arthur C. Clarke in particular) where a spaceship's propellant mass and energy are given as delta-v with units given as c (the ship was carrying 2.5c of delta-v, meaning it could alter its velocity a total of 2.5 times the speed of light accelerating and decelerating before running out of maneuvering ability.) We talk about fuel range in miles or km for cars -- but in minutes for aircraft. Units depend on usage. (part of why Bitcoin will never be a thing is that nothing will EVER be priced in bitcoin, it is not a convenient unit of account, nor will it ever be a stable one.) There will NEVER be one universal system of units to rule them all.
And then really, almost nothing is constant. Supposedly the distance between two stationary objects is a function of the age of the universe. The passage of time is influenced by the velocity at which you are travelling. Mass too is a function of velocity (the mass of the proton involved in a cosmic ray can be several kilograms viewed in a particular frame of reference.) Distance too is a function of velocity ( at v approaching c distances measured perpendicular to the direction of travel are not the same as those measured parallel to it.) g changes as you move away from the center of the earth. And on it goes. and on, and on.
Reality does have some constant, unitless numbers embedded in it, but they generally don't lend themselves to the construction of systems of units that are convenient to use. We do try to count where we can, rather than bulk (Avogadro's number) But nobody is purchasing bread flour in mols. So, I don't think trying to replace SI units is an exercise in anything but futility.
- #43
olgerm
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Firstly your post is factually incorrect.
- "Supposedly the distance between two stationary objects is a function of the age of the universe." It means that the distance is not constant, but word "constant" has different meaning here than in phrases "dimensional physical constant" and "mathematical constant". In this context it is an adjective, but in phrases "dimensional physical constant" and "mathematical constant" it is a noun. So this claim is misleading.
- "The passage of time is influenced by the velocity at which you are travelling". The word that you meant is "frame-invariant", not "constant". And even if you replaced word "constant" to "frame-variant" the whole claim would still be incorrect.
- "Mass too is a function of velocity". It is also somewhat a question of notation(terminology), but I would say it is not correct to call "relativistic mass" just "mass". "mass" should mean "restmass". If "mass" meant "restmass" here, then the whole claim is incorrect. And the word that you meant is "frame-invariant" not "constant".
- "Distance too is a function of velocity". The word that you meant is "frame-invariant" not "constant".
- "g changes as you move away from the center of the earth." The word that you meant is "homogeneous" not "constant".
In my idea for unitsystem I tried to get rid of arbitrary numbers (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom). In my unitsystem all dimensional physical constants are mathematically expressable (for example ##F_G=2^{-1}*(2\pi)^{-1}##). There are still unitless contants, but these are also not related to unitsystems - these are same in every unitsystem. By the way these unitless contants might also be mathematically expressable, but it is currently unknown whether and how.
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- #44
N1206
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I will admit freely that I don't understand your reply. Metrology is the study of measurement. One of the base requirements of a system of metrology is a system of units that all users can agree to. What is fundamentally impossible is to define a system of units that does not have some base, arbitrary assumptions to it that all the users agree and subscribe to. SI has base units that all others are derived from. Length is the distance between two points. If the inflation theory of the universe is correct, the distance between two points at rest to one another will have grown as time passes. So how then can you define an invariant unit of distance? Relativity means that all measurements of time and distance must necessarily be influenced by the conditions of the observer. A muon has a lifetime of ~ 2.2 µs at rest. Whistle the sucker up to 99.99% of c and its lifetime can be several seconds. Two atomic clocks, one left on the ground and one flown on an aircraft, will diverge in their measurement of time.
"I tried to get rid of arbitrary numbers..."
You can't. There will ALWAYS be a certain amount of arbitrariness to metrology.
SI has reduced that to seven items.
You may not like <how> the arbitrary items are defined by SI, and may want set the base value to some other arbitrary number--but it will be arbitrary.
Even our number system. We have ten fingers and have built a positional-notation system on base-10. There are good arguments that base-12 would have been better. The Mayans did base-20. The Babylonians did base-60. Computer guys do binary, octal and hexidecimal. You can do logarithms in base 10, but all logs can be reduced down to base e. Should we redefine "1 =e" as a good idea? Or what about "1=π"?
It is ALL arbitrary.
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- #45
olgerm
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I proposed an idea for unitsystem, but I do not have power force everybody to use it. And I have not claimed to have it.
Maybe, but my tried to make as simple and "unarbitary" unitsytem as possible. aka make all arbitrary choices that I had to make as simple as possible.
I do not have clear general mathematical method to compare which of 2 notations or unitsystems have less arbitarity in it, but despite o f that some notations have more arbritarity in them and some less. For example: Imagine a unitsystem, that which unit of length is defined as ## l_u=a_1*(sin(a_2^4*a_3^{-1}*a_4^{-3}))^{a_3/a_1} ## , where
- ##a_1## is tallness of Julius Caesar.
- ##a_2## is distance between Earth and Mars at time when Julius Caesar became consul for 1. time.
- ##a_3## is distance between Venus and Pluto at time when Julius Caesar became consul for 2. time.
- ##a_4## is length of left hand ofJulius Caesar.
You have clearly very big misunderstanding here. Some quantities have different values in different frames of reference or at different times, but I do not even understand why you think that it is related to unitsystems. I already explained that in post#43:
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- #46
Melbourne Guy
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I can't speak for others, @olgerm, but I did not intend to suggest you have that power...because if you did, I'm assuming we're all be using 'olgerms' already 🤣 Being serious, most posters on PF seem to be able to separate the idea from the person proposing it!
- #47
N1206
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The choices are ALL arbitrary, SI's, yours, the Julius Caesar example you proposed, or any other system. Two sets of arbitrary fought it out when CGS and MKS went toe-to-toe. In North America, SI and imperial duke it out on a daily basis.
"Even if some value is different in different times, different frames of reference or different locations, it is still measured in same units"
In the old days, when a foot was an actual ruler's foot, each time the king dies, the definition of the foot changed. What was 1'1'' could be come 11" the next day. Or if you crossed the border into a new king's territory. Napoleon recognized that this was an impediment to trade and that there was a vast plethora of units in use across his empire--and he put an end to most of them.
It is important that the unit NOT change.
https://en.wikipedia.org/wiki/International_Prototype_of_the_Kilogram
https://en.wikipedia.org/wiki/History_of_the_metre
https://en.wikipedia.org/wiki/Second
But given we live in a universe where inflation, relativity and Heisenberg's Uncertainty Principle reign, it has to be recognized that even the SI definitions of the seven base units are not completely static, but depend, however slightly, on the place and time in which they are situated.
Unit systems are judged on their usefulness in helping people communicate with one another. I truly don't understand how your proposed system would be more useful that what we have now.
- #48
olgerm
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Binary would be "least arbitrary", because 2 is the smallest number that can be base.
It is different, because ##e## and ##\pi## are not physical constants with unit (dimensional physical constants).
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- #49
olgerm
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Some unitsystems are more "simple", "mathematically beautiful", "natural" or "less arbitrary" than others.
I am not proposing a new SI version, but a new unitsystem.
I am not sure, but I think these are static. Write an example, where a SI-unit and my_post#13-unitsystem unit depends of place and time.
I wrote good properties of this unitsystem to post#13:
- #50
olgerm
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You have not written an example where SI-unitsystem unit or my_post#13-unitsystem unit depends of place and time in which they are situated. Do you still think that these units depend of place and time or you do not think that anymore?
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- #51
N1206
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The wavelength of the cosmic background radiation is now ~2 mm (millimeters)
It started at ~500 nm (nanometers) when the universe first became transparent.
Something you measured as 1 m long at the beginning to the universe is now ~4000 m long.
We, at the end of things, measure something by bouncing photons off it and interpreting their return.
The Uncertainty Principle shows that we can either pin down an object's position with great precision, or pin down its energy, but in either case our precision hits a boundary that we can never exceed, so how long something is can never be exactly measured.
So too, the units that we define cannot be used beyond a certain level of precision.
And then there is relativity. An observer traveling as significant fractions of c will not perceive events in the universe the same as an observer at rest...and neither of them are wrong. An item you perceive as being a meter long or an event being a second in duration depends upon your velocity in relation to the item or event.
You may think that it is semantics, that the unit has remained constant and that the object or event has changed, but it is not semantics. A unit system is peculiar to the time and place of its users and its usefulness to them in agreeing upon what they perceive. When they are NOT in the same time and place, adjustments become necessary.
https://physicscentral.com/explore/...elativity by,functions within about 2 minutes.
I don't know how the GPS units make their adjustments--by shaving off a number of clock ticks, or by saying that each clock tick actually measured more time (stretching the unit) But given that the ticks are what is counted, I reckon they have actually adjusted the units.
It started at ~500 nm (nanometers) when the universe first became transparent.
Something you measured as 1 m long at the beginning to the universe is now ~4000 m long.
We, at the end of things, measure something by bouncing photons off it and interpreting their return.
The Uncertainty Principle shows that we can either pin down an object's position with great precision, or pin down its energy, but in either case our precision hits a boundary that we can never exceed, so how long something is can never be exactly measured.
So too, the units that we define cannot be used beyond a certain level of precision.
And then there is relativity. An observer traveling as significant fractions of c will not perceive events in the universe the same as an observer at rest...and neither of them are wrong. An item you perceive as being a meter long or an event being a second in duration depends upon your velocity in relation to the item or event.
You may think that it is semantics, that the unit has remained constant and that the object or event has changed, but it is not semantics. A unit system is peculiar to the time and place of its users and its usefulness to them in agreeing upon what they perceive. When they are NOT in the same time and place, adjustments become necessary.
https://physicscentral.com/explore/...elativity by,functions within about 2 minutes.
I don't know how the GPS units make their adjustments--by shaving off a number of clock ticks, or by saying that each clock tick actually measured more time (stretching the unit) But given that the ticks are what is counted, I reckon they have actually adjusted the units.
- #52
olgerm
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So you think that length of meter is now 4000 times smaller than it was then? So for example distance between hydrogen atoms in hydrogen molecule (##H_2##), which is now ##7.4*10^{-11}*m##, was then ##1.85*10^{-14}*m##?
What do you think is exact function to calculate length of meter at any time? Do you think it is inversely proportional to wavelength of the cosmic background radiation ##l_{meter}(t)=(l_{meter}(t_0))^2/l_{wavelength\ of\ the\ cosmic\ background\ radiation}(t)##?
How does that make you think, that SI-unitsystem units are different in different places and times?
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- #53
N1206
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You seem to be missing my point.
Consider an observer directly underneath a geostationary satellite on the equator.
Both measure the length of one day, from noon to noon, in seconds with identical atomic clocks.
Their measurements will not concur.
Consider a being who created 'le grand metre' out of iridium at the beginning of the universe, entered stasis, and measured his 'le grand metre' now. The measurements will not concur.
So what good was the precisely defined unit, then?
You can define a set of units to be static, but the universe you use them on is not static.
Something winds up getting adjusted.
Consider an observer directly underneath a geostationary satellite on the equator.
Both measure the length of one day, from noon to noon, in seconds with identical atomic clocks.
Their measurements will not concur.
Consider a being who created 'le grand metre' out of iridium at the beginning of the universe, entered stasis, and measured his 'le grand metre' now. The measurements will not concur.
So what good was the precisely defined unit, then?
You can define a set of units to be static, but the universe you use them on is not static.
Something winds up getting adjusted.
- #54
gmax137
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- #55
Mike S.
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The most welcome of the SI unit changes is already underway, but stealthily. You may not know it, the physicists here might even disagree with me, but the ampere is already among the walking dead - a nonstandard unit for 1/96485.3 mol charge/second. (Mol charge can be written as "Eq" if you like). All the electrical units can be replaced this way. Eventually you'll be flipping a 0.2 mmol/s circuit breaker! Couldn't happen too soon. :)
- #56
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Yes, because metal evaporates over time so the bar will erode over such timescales, even neglecting that the early universe was a very hot place and iridium wouldn't be solid at an early enough time. Not because of the expansion of the universe, though.
- #57
Nugatory
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You’ll hear that a lot, but it is not correct. The uncertainty principle places no limit on how precisely a quantity can be measured; you get as many decimal places of precision as your measuring instruments are good for. It is true that…
but that is not because of the uncertainty principle. It’s because no matter how good our instruments are, there’s always room for further mechanical improvement.
That was the case with the traditional definitions based on reference objects, but not with the new SI definitions. The modern definition of the meter, for example, specifies a length that can in principle be measured to arbitrarily great precision so can never be obsoleted by improvements in our measuring instruments. The better our instruments, the more exact our meters.
This is quite unlike a standard based on some reference artifact; for example a reference meter bar can never be more exact than the inevitable fluctuations in its length as atoms on the surface go walkabout. Were our measurement technology to improve enough to detect these fluctuations we would find ourself unable to say what a meter “really” is, just that it’s somewhere between the extremes of the fluctuations.
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- #58
olgerm
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It is not because length of units is different in different places or times, but because length of time between same events may be different in different frames of reference.
Meter is not defined by prototype metre bar (etalon) anymore. Even if length of some metal bar changes, length of meter would not change.
Suggested for: Replacing the Measurement standards (SI units)
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