Latest posts on math thread topichttps://rhizzone.net/forum/topic/14538/2020-05-28T19:26:18+00:00Discussion :: Laissez's Faire :: math thread (by cars)
2020-05-28T19:26:18+00:00399480*gesturing at my unit*
Discussion :: Laissez's Faire :: math thread (by liceo)
2020-05-27T21:15:54+00:00399443impressive thank you
Discussion :: Laissez's Faire :: math thread (by toyot)
2020-05-27T16:42:58+00:00399440it's whatever's used in development of the communist material condition, the transition from agriculture to machine autotrophy, a new species-niche for us. the new species-niche replaces the over-winter surplus the parasite classes were born feeding from, with continuous food molecule production, bonds of these starches and lipids holding any source of energy which can make rotational energy, to turn pump shafts, compressors, valve states, impellers. the design of it needs numerate communists. unless the state-lumpen joins the new class, because there is no surplus food to tax or steal, the cop will die by starvation and his class with him. if he steals the machine, then that is his last act in his old class. if he uses his hands and mind for something useful for once, like constructing it, then he's decided to leave his old class. same to the booshwazee, who will run into trouble filling the factory, without their class controlling the food surplus and regulating our access to it with money. as marx said, if workers could eat from the air, then there would be no need for the wage.
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<br/>what did you think of the magnitude algebra system?
Discussion :: Laissez's Faire :: math thread (by liceo)
2020-05-27T12:46:14+00:00399438what is the formula that kills all kkkops?
Discussion :: Laissez's Faire :: math thread (by toyot)
2020-05-26T23:18:13+00:00399430
<br/>
<br/><div class="code"><pre>
<br/> Power of 10 | +Name | -Name | Symbol | Other names
<br/>
<br/> 10^0 0 | 1 | 1 | numbers | one
<br/> 1e(1*3) 3 | Kilo | ka | K & k | one thousand(th), kilo/milli
<br/> 1e(2*3) 6 | Mega | micro | M & m | one million(th), mega/micro
<br/> 1e(3*3) 9 | Giga | gano | G & g | one billion(th), giga/nano
<br/> 1e(3*3*3) 27 | Wo | wa | W & w | one billion-billion-billion(th), GGG, ggg
<br/> 1e(2) 2 | Hundred | percenti| H & % | Most languages have a simple, short word for 100
<br/>
</pre></div>
<br/>
<br/>exploring this more:
<br/>
<br/></p><blockquote><p class="postbody_text">in an algebraic equation, we could quickly count all kilo's, mega's and milli's, and determine the calculation's magnitude. a pressure of 1 kg / 1 mm / second^2 : 1 kilo / 1 milli = 1000 / .001 = 1,000,000 pressure ... the <em>right </em>half of the unit's name reveals the final unit's physical nature, and the <em>left </em>half, its final order of magnitude. </p></blockquote><p class="postbody_text">
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<br/>the prefixes for thousand/million/billion can cover a lot of number territory in combination, if 'combination' is interpreted as multiplication. a megakilo is equal to a giga, (thousand*million=billion), a kilokilo = mega, a megamicro = 1 (a million/a million=1), kakilo = 1, gigagiga = 10^18, ganogano 10^-18. 97.3 percentimeter is 97.3% of a meter, 97.3 current centimeters.
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<br/>in symbols, 1/k = K, and 1/K = k. and K/K = k/k = kK = Gg = 1,000,000,000 * 1/1,000,000,000 = MMmmMmgG = 1. and g^2 = gg.
<br/>
<br/>a mole, ~6.02*10^23, would be ~0.602 Megagigagiga, 10^9 * 10^9 * 10^6 => 9+9+6 = 24, or 0.602 MGG. a value like 18 g/mol molecular weight of water, is converted to 0.018 kg/mol => 18/0.602 k/MGG => kmgg => ggg => 30 wamass ('wa', equal to 10^-27, is a prefix useful for putting mass into molecular weight ranges, without invoking a ridiculous number like 6.023e23. 'wa' is from quechan for baby, 'wawa'. a wawa is a very tiny number.)
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<br/>the diameter of the observable universe is ~1 wometer, the diameter of the galaxy is ~1 microwo meter, (because it is 1/1,000,000 the diameter) and the planck length is ~0.16 wagano meter. a lightyear is around 9.4 MG meters. the age of the universe is 13.8 billion years, or gigayears, and with 31.54 megaseconds in a year, it's (31.54 * 13.8) MG seconds old, ~0.3 GG seconds, (~0.3 billion billion seconds). 0.3 woseconds is the age of the universe in nanoseconds. the atomic mass unit is 1.66 wa of mass (whatever we decide to name the mass unit, equal to 1kilogram). 0.1602 gg energy = 0.1602 * 10^-18 = 1 eV. i mean this to say, we can more easily lose units named after western scientists, and lose these very large and very small ridiculous numbers and constants. 10^(3*3*3) meters is 1 universe diameter, 10^-(3*3*3) is the order of the mass of a proton. taking advantage of this coincidence in powers of ten, will help both fields use the same unit system without invoking numerous constants. an exponent word system which traverses up to 54 orders of magnitude (w/W) using 10^(3*1), 10^(3*2), 10^(3*3), 10^(3*3*3), 10^(2), and their inverses: it could be possible to give a name to any order of magnitude between 10^-70 and 10^70 using 1 to 4 letters, with a magnitude algebra that behaves similarly to the existing unit algebra.
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<br/>
<br/>
<br/>Working a problem with very large and very small numbers: how many atoms of oxygen there are in the atmosphere?
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<br/>at sea level in SI, there is 101325 pressure. pressure is force divided by an area. we know the second law of mechanics defines force as F=ma. force=mass*acceleration, force=mass*distance/time/time. 101325 pressure = 0.101325 Mpressure.
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<br/>all the atoms of atmosphere above each square inch of the earth weigh 14.7 pounds, or in SI, have mass of 101325 kilograms times gravity's 9.81 m/s^2 acceleration. to convert a force into a mass, divide by its acceleration, m=F/a.
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<br/><div class="code"><pre>
<br/>0.101325 Mpressure / 9.81 meters/second^2 of gravity
<br/>= (0.101325 / 9.81) * M * pressure / meters/second^2
<br/>= (0.101325 / 9.81) * M * mass / area (by F=ma)
<br/>= (0.101325 / 9.81) * M * mass / (meters^2)
</pre></div>
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<br/>this calculates the total mass of atoms compressing us from above, every square meter. we convert total mass, into the known % of atmospheric oxygen, to determine number of atoms of oxygen, per sqm:
<br/>
<br/><div class="code"><pre>
<br/>= (0.101325 / 9.81) * M * mass / (meters^2) * 21% oxygen mass/100% total mass
<br/>= (0.21 * 0.101325 / 9.81 ) * M * %/% * mass oxygen / m^2
<br/>= (0.0022) * M * units, and 0.001*M = K
<br/>= 2.2K mass of oxygen/m^2
</pre></div>
<br/>
<br/>To find # of atoms, determine the mass of an atom of oxygen:
<br/><div class="code"><pre>
<br/>molar weight of oxygen = ~18 g/mol
<br/>1 mole = a huge number equal to 6.02*10^23 = 0.602 MGG
<br/>1 gram = 1/1000 mass units
<br/>
<br/>Mass of an atom of oxygen = 16 g/mol
<br/>= 16 grams / (mole of oxygen)
<br/>= 16 grams / (0.602 MGG oxygen)
<br/>= 0.016 mass / 0.602 MGG oxygen
<br/>= (16 / 0.602) k/MGG mass/oxygen
<br/>k/MGG = kmgg = ggg = w
<br/>= 26.6 ggg of mass per atom of oxygen, or 26.6 wamass. very small.
</pre></div>
<br/>
<br/>the mass of the total oxygen over each sq.meter of land & water, is 2K mass (2,000 in today's kilograms). and we found the mass of the oxygen atom in kilograms, by converting from moles, 30 wamass/atom.
<br/>
<br/><div class="code"><pre>
<br/>(2.2 K mass / sq.meter) / (26.6 wa mass / atom )
<br/>= (2.2 / 26.6 ) K/w (atoms * mass / mass)
<br/>= 0.083 KW atoms
<br/>= 83 KkW atoms per sq.m
<br/>= 83 Wo atoms per sq.m (a wo is very big)
</pre></div>
<br/>
<br/>the second-to-last step is to estimate the surface area of the planet.
<br/>
<br/><div class="code"><pre>
<br/>Diameter of earth = 12.7 M meters
<br/>Surface area of earth = (4 * pi * 12.7 * 12.7 / 4 ) MM sq.meters (M^2 = MM)
<br/>= ~510 MM sq.meters
<br/>= 510 trillion sq.meters
<br/>= 0.51 GM sq.meters
</pre></div>
<br/>
<br/>Finally multiply atoms per sq.meter, by total sq.meters, to get total atoms of breathable oxygen:
<br/><div class="code"><pre>
<br/>0.51 GM sq.meters * 83 W atoms / sq.meter
<br/>= 42 WGM atoms of oxygen in atmosphere
</pre></div>
<br/>
<br/>to summarize, when we finally graduate out of inches pounds and miles, we can jump to SI's fixed measures for global measurement compatibility but use our own names for things. a unit system is a system of physical quantities, names of the quantities, and a system of words for numbers, like tera, yotta, nano, mole. SI's words for numbers are a mess, because the metric system was invented before modern cosmology and atomic physics. a good unit system should unify measure in cosmology and particle physics. but the wide use of extreme special constants, like the mole, eV, AU, lightyear, means SI fails at these extremes. and its words for units are scientist names. we can join the world in SI, and in our language, rename some units so to better traverse the magnitudes of physical number from planck's constant (0.662 wamicro energy-seconds), to the number of atoms of oxygen in the atmosphere. the words for thousand,million,billion divide like their units do, so this is a magnitude algebra that a working person can operate in parallel to the unit algebra.
Discussion :: Laissez's Faire :: math thread (by toyot)
2020-05-06T19:54:52+00:00398719it's fun to think about. units get philosophical. let me see...
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<br/>you're right, 'distance' should not refer to a fixed distance, like a 'light-year' or 'meter'. in a unit system, there are fundamental units -- distance, time, mass, charge... the fundamental units should have names separate from their concepts. but once mass, time, and distance are defined, then there is a natural '1' of pressure: one mass / distance / time / time. so, when the unit system is declared, on the engineering drawing or page of calculations: it is unambiguous what 1 pressure or 1 energy means (but it is ambiguous, what '1 mass' or '1 distance' means, so these need specification: because they ARE the unit system).
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<br/>yea for unit algebra, you're right it's better if people wrote N/m^2 (or kg/m/s^2), especially when first learning, or performing a complex conversion... nothing is verboten, but, breaking derived units down to fundamentals, can also introduce error: if pressure is incorrectly rendered N/m once, then the benefit of the unit algebra is lost, until the error is discovered. the more symbols that need to be in a specific combination, the more chances for error. it's up to the person performing the work. sometimes we want to explicitly name a quantity 'pressure' or a unit like 'bar', without deriving it. that's okay too.
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<br/>it's never bothered you that the kilogram is the only SI fundamental unit with a prefix? it always bothered me... if 1 new gram = 1 kilogram, then the density of water becomes the simpler 1 g/L. today it's either 1 kg/L, 1 g/mL, or 1000 g/L. if with your suggestion, the base unit of mass became today's gram, though, then everything would shift. 1 joule becomes 1 millijoule... but here's a better reason than aesthetics & saving ink: the SI naming inconsistency actually disables a <em>second </em>potential unit algebra: if we only just drop the 'kilo' from kilogram, then in an algebraic equation, we could quickly count all kilo's, mega's and milli's, and determine the calculation's magnitude. a pressure of 1 kg / 1 mm / second^2 : 1 kilo / 1 milli = 1000 / .001 = 1,000,000 pressure (try this today and everything is off by 1000^n mass terms). by accounting prefixes, we can determine an answer's order of magnitude. a whole secondary unit algebra is possible if we re-name the SI kilogram. using unit algebra, the right half of the unit's name reveals the final unit's physical nature, and the left half, its final order of magnitude.
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<br/>the mole is just a big number 6.023e23 and the emole is another number, 6.24e18. the mole was fine-tuned, mass assigned to the nucleons, semi-arbitrarily, to keep 1kg/L~=density of cold pure water. the 'emole' (coulomb) was also fine-tuned, but so that the formula P=IV works. one emole per second, times one epressure, equals one power. or 1 eflow times 1 epressure, equals 1 power. in hydraulics, flow*pressure=power. but the circuits i build, are not complicated, like household plumbing compared to a chemical plant. what are some good or better names, do you think, 3 syllables or less, easily abbreviated, pedagogical, for what happens in a circuit?
Discussion :: Laissez's Faire :: math thread (by c_man)
2020-05-06T19:21:24+00:00398718my feelings about units are that the metric is fine except that celsius is worse than fahrenheit for everyday use, and if youre not talking about everyday use you can just use kelvin
Discussion :: Laissez's Faire :: math thread (by tears)
2020-05-06T09:48:31+00:00398693some things to think about:
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<br/>if you were simplifying units surely the first thing you would do is to strip out stuff like pascals and bar all together and just express it as N/m<span style="position:relative;bottom:0.5em;">2</span> or MN/m<span style="position:relative;bottom:0.5em;">2</span>. it would help with understanding - same for watts as J/s
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<br/>i dont understand why you would rename kilogram to gram when there is already a quantity of mass called a gram - i could understand if you wanted to switch the SI unit of mass to the quantity denoted by a gram - that would be cool, since the use of the kg is just some historical quirk. then kilogram would just be the unit + the prefix like everything else
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<br/>i dont like the term electron pressure to refer to p.d. because it brings in all sorts of misconceptions - electricity is one of the hardest things to teach and i have used plenty of water flow metaphors, but they tend to come back and bite you - since volts are just joules per coulomb i think that is a far better way to unit it - since it is very descriptive as energy per packet of charge -> i also find it helps with visulisation in terms of energy transfer. The problem does build with this since converting derived units back to SI units is pretty hard when you get to things like ohms - V/A, which would then be (J/C)/A or J/(A<span style="position:relative;bottom:0.5em;">2</span> x s) or whatever which quickly gets complicated - expressing units in terms of other units and back to SI units tends to get left to A-level physics here
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<br/>i also dont like the term eFlow for rate of flow of charge, just because it uses an e, which tends to get associated with electrons, and charge flow is charge flow not necessarily electron flow - i know that e is used for elementary charge but theres a big difference between teaching elementary charge at A-level and teaching flow of charge to 12 year olds who cant write good.
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<br/>i can see problems with relating quantity of charge to moles in the eMole for coulombs and moles for amount, unless you were to redefine one or the other so that the mole part refereed to the same number of particles and elementary charge multiples - which you could do - it would be quite nice to standardise
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<br/>im not against renaming units, i just think that ease of learning is paramount
Discussion :: Laissez's Faire :: math thread (by Gssh)
2020-05-06T05:07:52+00:00398686this is good, but is still in english.. which is bad. better to use esperanto as starting point.
<br/><div class="code"><pre>| Nova Nomo |
<br/>| Energio |
<br/>| Potenco |
<br/>| Forto |
<br/>| Metro |
<br/>| Litro |
<br/>| Gram |
<br/>| Dua |
<br/>| Temp |
<br/>| Lumen |
<br/>| Stango |
<br/>| Premo |
<br/>| Turnu |
<br/>| eFluo |
<br/>| ePremo |
<br/>| Om |
<br/>| eMole |
<br/>| Mole |
<br/>| Persekundo |
<br/>| ? |
<br/>| ? |
<br/>| Zum |
</pre></div>
Discussion :: Laissez's Faire :: math thread (by Belphegor)
2020-05-06T03:44:34+00:00398685I'm torn between tears pedagogical argument and the coolness of smoothing out the unit names
Discussion :: Laissez's Faire :: math thread (by tears)
2020-05-05T20:57:38+00:00398657it doesnt seem to work since you have the unit the same as the quantity so in your algebra, for energy you would have E(nergy number) quantities of E(nergy unit) (E x E) rather than the current system which is E x J (or eV or whatever unit you are using) it makes it confusing and makes it even harder to understand that the units are arbitrary quantities of a concept and can be any value (imagine you had the following units of distance: 1) metre, 2) light year 3) distance; each one being a different distance in space)
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<br/>sorry, i am immediately thinking of the teaching nightmare having the name of the concept and the name of one of the the units for the concept being the same!
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<br/>edit: i am mad about the volts thing - having volts as a unit, and having "voltage" used as a catch all to refer to p.d./e.m.f. is tough to deal with
Discussion :: Laissez's Faire :: math thread (by toyot)
2020-05-05T20:42:05+00:00398655when the cultural revolution here sweeps away the old society, including the inch-pound system, and we join the rest of the world proletariat with metric, a small suggestion to decolonize the units. students today have to learn two things, the concept of "force", "energy", "electric potential", and a dead european's name. just call things "3.5 force", "2 energy".
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<br/><div class="code"><pre>
<br/>Old Name| New Name |
<br/>Joule | Energy |
<br/>Watt | Power |
<br/>Newton | Force |
<br/>Meter | Meter |
<br/>Liter | Liter |
<br/>Kilogram| Gram |
<br/>Second | Second |
<br/>Kelvin | Temp |
<br/>Lumen | Lumen |
<br/>Bar | Bar |
<br/>Pascal | Pressure |
<br/>Degree | Turn, Rev|
<br/>Ampere | eFlow |
<br/>Volt | ePressure|
<br/>Ohm | Om |
<br/>Coulomb | eMole |
<br/>Mole | Mole |
<br/>Hertz | Persecond|
<br/>Henry | ? |
<br/>Weber | ? |
<br/>100watts| Hum |
</pre></div>
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<br/>- finally discard the babylonian 360-degree circle, for the 'turn' or 'revolution', 1 equal to 360 degrees or 2pi rad. this unit is already in wide use in cars and machine tools, but not in trigonometry.
<br/>- rename the electric units to their hydraulic analogy, which has some pedagogical value. the name 'volt' etc isn't useful in a library since nobody's learned from his writings in a century. decolonize ohm to om since its symbol is capital omega. there might be better options than this but it isn't retaining the existing names of these units.
<br/>- one additional unit, the hum. like the bar is a 'metric' approximation to earth's air pressure a bit above sea level, the 'hum' is exactly 100 watts, equal to 2066 food calories per 24 hours. when we buy a bag of food, or whatever our relationship to our food is in the future, we shouldn't need to do 3-digit multiplication, calories by serving size, to eat it healthily & figure out what we bought. if it contains 1 hum*day, you can eat 1/3 of it over 3 days. 86 calories is 1 hum*hour. i just mean, i think it's a good idea. while we're changing everything, let's change that too.
Discussion :: Laissez's Faire :: math thread (by c_man)
2020-05-05T16:56:34+00:00398644You're certainly right in that its very easy to hide energy is all sorts of ways and you cant tell how much energy there is in some volume of space just by looking at it, as opposed to something like momentum or electric current which can be immediately identified. If there's a net momentum to some collection of matter it will be immediately obvious since the whole thing will be moving. The fact that you cant immediately identify all of the operative modes of energy distribution in some region of spacetime is one of the things that makes physics hard, and is in part why its often understood by its practitioners as an exercise in modeling the world as opposed to an identical description. Most of the models in physics end up taking the form of some proposed energy function, along with very particular rules for how this energy function induces dynamics. An energy function could account for all of the things you mention: isotropic strain, torsion, rigid motion, heating, electric charge, etc. An important principle of practice when studying these systems is that "anything that is not forbidden is mandatory". What this means is that any type of interaction between different types of energy ought to be considered unless it is forbidden by some superseding principle (e.g. some type of symmetry, experimental setup, material conjecture, separation of scales, or the impatience of the person doing the math). That is to say, for each type of energy that is embedded in some body, there is usually a way for it to be converted to each other type (although this can be ignored if, say, it takes a much longer time than the duration of interest).
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<br/>On the topic of volume, though, its important to note that its very possible to change shape without changing volume. This is what every incompressible fluid does when it moves around, and is also the type of deformation described by a "pure shear" of some solid body. It's important not to confused the derivative of the volume (dV/dt, a single number) with the total set of derivatives of the individual material elements (the set {dX_i/dt} of the derivative of each displacement vector X in each direction i, d*N numbers where d is the spatial dimension and N is the number of material elements in the solid).
Discussion :: Laissez's Faire :: math thread (by toyot)
2020-05-05T07:39:35+00:00398619thank you for the dimensional analysis argument. i think that makes sense. thinking more, the relationships between distances inside a body, is more complicated than could be conveyed in just some amount of joules. using the same amount of energy, there's more than one way to change the distance between any two points, inside a solid or flexible body. a metal body can be compressed to hold say 10 joules of energy, or can be torsioned to 10J, or heated with 10J of energy to cause thermal expansion, or a 10J sound wave can be sent thru. all these will change the distances between particles in unique ways. so, whatever's going on, can't be accounted for by just change in energy. thinking about it more, interpreting the observation of the '7th DOF' as a volume change, makes much more sense. dV/dt of a solid body = 0 when it's not put under strain, or undergoing thermal expansion. so it captures that. when dV/dt = dθx/dt = dθy/dt = dθz/dt = dx/dt = dy/dt = dz/dt = d(space itself)/dt = 0, then all the distances, between all points on the surfaces of two solid bodies, are fixed, and the two parts are exactly constrained.
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<br/>interestingly, it's not the volumes of the two solid bodies, it's some special volume, perhaps made from the 6 points of contact. a solid body can have a chunk removed from it in a non-contacting region, change its volume, and the kinematics will stay the same. only contact points are important, maximum 6.
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<br/>there isn't a preferred or natural volume made by 6 points. maybe an octahedron, but there's no obvious way to decide which points, connect to which points to form it.
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<br/>6 points:
<br/>a,b,c,d,e,f
<br/>
<br/>6 points can make 15 distances:
<br/>(with ab = -ba)
<br/>ab,ac,ad,ae,af,
<br/>bc,bd,be,bf,
<br/>cd,ce,cf,
<br/>de,df,
<br/>ef
<br/>15 total = triangular(n-1)
<br/>
<br/>6 points can make 60 parallelograms:
<br/>(with ab^ac = -ac^ab = ac^ba = -ab^ca, and ab^ab=0 etc, the wedge algebra)
<br/>ab^ac, ab^ad, ab^ae, ab^af,
<br/>ac^ad, ac^ae, ac^af,
<br/>ad^ae, ad^af,
<br/>ae^af,
<br/>
<br/>ba^bc, ba^bd, ba^be, ba^bf,
<br/>bc^bd, bc^be, bc^bf,
<br/>bd^be, bd^bf,
<br/>be^bf
<br/>.
<br/>.
<br/>..etc
<br/>6*10 = 60 total
<br/>with 5 it would be 5*6 = 30
<br/>with 4 it would be 4*3 = 12
<br/>formula is n * triangular(n-2)
<br/>
<br/>6 points can make, i believe by coincidence, again 60 unique parallelopipeds:
<br/>ab^ac^ad, ab^ac^ae, ab^ac^af,
<br/>ab^ad^ae, ab^ad^af,
<br/>ab^ae^af,
<br/>
<br/>ac^ad^ae, ac^ad^af,
<br/>ac^ae^af,
<br/>
<br/>ad^ae^af
<br/>
<br/>Checking if it's possible to make more, by branching the 3rd vector off the end of another leg, instead of all vectors from a common origin:
<br/>ab^ac^ad =? ab^ac^cd
<br/>cd = ca+ad
<br/>ab^ac^cd = ab^ac^(ca+ad) = ab^ac^ca + ab^ac^ad = 0 + ab^ac^ad
<br/>So w/o checking them all i believe that the formula, for the # of unique parallelopipeds made from n points, is
<br/>n * tetrahedral(n-3)
<br/>
<br/>it makes sense that the n-minus-dimension pattern will run up the wedge algebra grades to eventually = n. 6 unique hypervolumes from 6 pts:
<br/>ab^ac^ad^ae^af,
<br/>ba^bc^bd^be^bf, etc
<br/>
<br/>but this probably isn't the right path. this reasons from just the locations of contact points, and not its force vectors, which better disqualify non-physical mechanisms, like when they intersect (a sphere can only be touched in 3 places, all intersect at the center; same with a plane at infinity; a turned part is 5C max since all C vectors intersect its centerline). and, there are valid mechanisms, like maxwell's 2-2-2 mount, where all the volumes as calculated above will be zero, since all contact points share a plane. so i'm probably barking up the wrong tree. fun to find any math pattern regardless.
Discussion :: Laissez's Faire :: math thread (by c_man)
2020-04-28T15:29:17+00:00398250this is where dimensional analysis helps. mathematicians call this combination x^y^z (with ^ indicating the wedge product), or xyz for short, a volume form because it has dimensions of volume, simple as that. if you have a parallelepiped or cuboid (like a 3d parallelogram or rectangle respectively) or similar simple 3d shape, the product of its three spatial dimensions is its volume. it's actually not a separate degree of freedom, but it is a different way of measuring something: you cant change the volume of some shape without changing its spatial extent in at least one dimension. in the same way a cuboid can be uniquely identified only in terms of its three dimensions. for more complicated shapes you have you use a differential measure and then integrate: dx^dy^dz. this is the standard little symbol you put in a volume integral behind the integrand to indicate that you want to measure all three dimensions at once, that is, that you want to measure volume. time actually doesnt come into this at all, and again you can tell this just from looking at the dimensions of the quantities we are considering: all have dimensions of distance, so there is no way for time to enter unless we introduce something else to our theory. for example, every theory of wave propagation has at least one implicit timescale. this introduces a quantity with dimensions of time and you have a whole new set of things you could want to measure. unless the theory is quite simple (i.e. a linear theory), there are actually a ton of different things you could want to measure and you have to be careful and precise about what you're interested in, etc.
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<br/>now, if you want to measure things in special or general relativity you introduce time as a coordinate with a different metric signature. then the total spacetime "volume form" has dimensions of volume times time.
<br/>
<br/>