Great Math Mystery
http://www.pbs.org/wgbh/nova/physics/great-math-mystery.html
just started watching it, some amazing stuff
for example, crazy stuff about pi, like:
Quote: below link which I was prompted to search for"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14, which is close to the value of the number pi... The ratio of pi is most commonly found for rivers flowing across very gently sloping planes, such as those found in Brazil or the Siberian tundra."
http://www.joyofpi.com/pifacts3.html
Many rivers do kinda look like a sine wave...
Still, you learn early on in your "philosophy of mathematics" course (which is really what the Nova show was about) that one of the big questions is "does 2+2 = 4 on mars?" In other words, is mathematics a human creation or does it exist in some fundamental way and is being discovered? Based on the content of the show, they seemed to be arguing the latter.
Quote: teliotIn other words, is mathematics a human creation or does it exist in some fundamental way and is being discovered?
Best to think it's our own idea.
Quote: teliotI watched the show. As a former professor of mathematics (15 years), they emphasized a point that is entirely off base for what mathematicians do - very little modern mathematics has anything to do with solving physical problems
the knowledgeable viewer's first hint is that he can watch and be entertained without doing any math LOL. That I can say is entirely beyond my actual experience in school, yes, absolutely.
Quote:It is pure abstract nonsense
wow, buzzkill!
Quote:Still, you learn early on in your "philosophy of mathematics" course (which is really what the Nova show was about) that one of the big questions is "does 2+2 = 4 on mars?"
Granted, a lot of the jaw-dropping stuff is on the order of noting that adding the digits of a number to get another number and ascertaining that if it is divisible by 3 then the original number is divisible by 3. If that goes somewhere profound I can't get there myself.
I nonetheless really liked the program
Human never "invented" math. They just learned to count, then the rest is history.
How can you not see GOD in -1=e^i*pi
Quote: teliotStill, you learn early on in your "philosophy of mathematics" course (which is really what the Nova show was about) that one of the big questions is "does 2+2 = 4 on mars?" In other words, is mathematics a human creation or does it exist in some fundamental way and is being discovered? Based on the content of the show, they seemed to be arguing the latter.
Didn't you watch Star Trek: the Next Generation, or the movie Contact? Both of them used a sequence of prime numbers as a sign of intelligence. Never mind that ST:tNG takes place in a future where they still hadn't solved Fermat's Last Theorem (or, for that matter, it no longer exists as everything after Enterprise was retconned by the new movies when Vulcan was destroyed and Spock's mother was killed when he was young).
The only way 2 + 2 is not 4 on Mars is if they use a Base 3 or 4 system. (If binary is used, then "2" would not exist.)
Quote: ThatDonGuyDidn't you watch Star Trek: the Next Generation, or the movie Contact? Both of them used a sequence of prime numbers as a sign of intelligence. Never mind that ST:tNG takes place in a future where they still hadn't solved Fermat's Last Theorem (or, for that matter, it no longer exists as everything after Enterprise was retconned by the new movies when Vulcan was destroyed and Spock's mother was killed when he was young).
The only way 2 + 2 is not 4 on Mars is if they use a Base 3 or 4 system. (If binary is used, then "2" would not exist.)
If they use base 3, '4' doesn't exist.
Not that it matters. 2+2=4... given a certain set of axioms that define integers, addition and equality. Hofstadter describes one in "Godel, Escher, Bach". One that doesnt require any base system. Just rules for manipulating symbols.
......
Knowing that number whose digits add to a multiple of three is also a multiple of three is useful when do math in my head. This rule is dependent on the base of the system. So theres probably some interesting number theory reason why. Math theories being practically useful happen in the oddest of places.
The word 2 as used in the "real word" is an adjective. The word "2" as used in the equation above is a noun. As an adjective, it is imprecise. As a noun it is exact. It is happy coincidence that the equation 2+2 = 4 also says something about the property of these adjectives, but it begs the question, what exactly are 2, +, = and 4 as nouns? What is the rule by which we substitute the noun 2 for the adjective 2 apples?
The meaning of 2, +, = and 4 as nouns is a human creation. The approximation that 2 apples + 2 apples = 4 apples is not. At some point in your education you went from 2 apples to 2. That was the leap in abstraction that moves math into its pure form.
So, does 2 + 2 = 4 on Mars? Is math created or does it fundamentally exist and is being discovered?
Quote: teliot...The meaning of 2, +, = and 4 as nouns is a human creation...
Exactly. They are nothing more than originally someone's opinion.
Some people might call this, "2", two. Some might call it dos. I might call it four!
Quote: telliotIn other words, is mathematics a human creation or does it exist in some fundamental way and is being discovered? Based on the content of the show, they seemed to be arguing the latter.
I think it is a purely human and abstract creation designed to fit the reality that we observe.
We can describe the things that we see mathematically, and are sometimes surprised when we find correlations between different things based on the math used to describe one thing, like fractals, conch shells, and this PI ratio of the length of a river.
But I think reality came first, and math came second, rather than math being the set of rules that reality follows when things form.
Is that what you meant?
The point of the Nova show was to explore the question. You chose an answer, that's good. But the question is much harder than you might imagine. Look up Bertrand Russel for the roots of the attempt to give it a good answer.Quote: Dalex64But I think reality came first, and math came second, rather than math being the set of rules that reality follows when things form.
Is that what you meant?
Those who use terms like "Math Bozy" and "Mathletes" take the point of view that 2 + 2 does not equal 4 on Mars. Likewise, those who argue about progressions or that simulations can't model the real world. This is a real and ongoing point of philosophical contention that plays out again and again. I just think the Nova show didn't do the question justice.
Thanks Don. 8)Quote: IbeatyouracesI think you meant to type "boyz" :-)
I don't think there is a "2" unless there is a "1". "1" is a singularity, distinguishable as a separate entity from all around it, complete in itself. But not unique in the world. If not unique, then there must be at least 1 other "1". So that requires a "2". And any grouping of singularities, even if each IS unique, as a subset of any larger entity, also requires a "2". But both cases refer directly to "1".
"+" is an indication that there is a larger world than the one in which the singularity exists. "1" is a subset of "world" when "world" is anything that includes more than the singularity (including how I used the word in the previous paragraph). "+" means that there is a commonality between singularities and/or groupings that can be conceptually understood as a larger grouping.
"=" is an indication that some characteristic of one singularity/grouping has a common equivalence with another, when examined from outside, a larger world. Short of the equation "everything = everything", anything that can be numbered is a subset of "everything". Anything, however grouped, on either side of "=" can be substituted for the other one, else it is a false equivalency.
But I haven't watched the show, so maybe I'm way off base on all of this.
If you want to be technically correct (sort of, a lot is missing here), 2 is defined to be the cardinality of the set {{},{{}}}, + is defined via a disjoint union binary operation, and = is an equivalence relation based on set cardinality. This all begs the question, "what is cardinality," which is a whole can of worms by itself to explain. There is really little debate about what these things are among mathematicians, the problem is to figure out why 2+2 = 4 is predictive of the behavior of apples.Quote: beachbumbabsI was kind of enjoying "Math Bozy" as a moniker, actually. :)
I don't think there is a "2" unless there is a "1". "1" is a singularity, distinguishable as a separate entity from all around it, complete in itself. But not unique in the world. If not unique, then there must be at least 1 other "1". So that requires a "2". And any grouping of singularities, even if each IS unique, as a subset of any larger entity, also requires a "2". But both cases refer directly to "1".
"+" is an indication that there is a larger world than the one in which the singularity exists. "1" is a subset of "world" when "world" is anything that includes more than the singularity (including how I used the word in the previous paragraph). "+" means that there is a commonality between singularities and/or groupings that can be conceptually understood as a larger grouping.
"=" is an indication that some characteristic of one singularity/grouping has a common equivalence with another, when examined from outside, a larger world. Short of the equation "everything = everything", anything that can be numbered is a subset of "everything". Anything, however grouped, on either side of "=" can be substituted for the other one, else it is a false equivalency.
But I haven't watched the show, so maybe I'm way off base on all of this.
Quote: andysif... "I AM THAT I AM".
Yes, as a self-defined inter-consistency of every thing. (Hint) Space-time operations for space and time.
For us, properly getting off our "high horses" in the manner while then consequently elevating the remainder of things for a good look. Pfft? Consider that we haven't begun to really figure anything out. We couldn't have been "THAT" smart after all.
Perhaps, it's not a problem/solution after all, but only another point of view. Not the shift from noun to adjective, etc, but the true whatness of the noun.
Quote: teliotThe word 2 as used in the "real word" is an adjective. The word "2" as used in the equation above is a noun.
This is outside the scope of mathematics.
In mathematics, 2 (and anything else) is defined based on some (few) agreed rules - Independent of your "base system" or planet.
These rules as so "simple" that any non-mathematician would shake their head for the level of stupidity these rules represent.
Anyway, as long as these few rules are accepted, the number 2 (not to confuse with the literal "2", the word "two" or its representations like "10" in binary systems) has the same properties and is the same thing.
On mars and elsewhere. Whether humankind found them or not.
Quote: MangoJ... These rules as so "simple" that any non-mathematician would shake their head for the level of stupidity these rules represent.
We could not access something so pure or uniform. But, the mental and physical come together effortlessly when the two are made up of the same stuff. As effortlessly as to give rise to such "rubs".
Physics doesn't do the numbers justice. Special relativity has 1+1 stuff at under 2; and, quantum stuff has to spin twice, eg, to turn once.
Does the math? What if the higher levels of infinity curl up in the same way? It does seem a harder or different math even when the regular numbers become much larger.
And, can't keep adding more and more apples, eg.
Quote: teliot
In other words, is mathematics a human creation or does it exist in some fundamental way and is being discovered? Based on the content of the show, they seemed to be arguing the latter.
I have been reading "Quantum Philosophy" by Robert Ormes - which is concerned with this question and the reconciliation of quantum physics with the physical world that our senses reveal to us. Ormes argues pretty convincingly that mathematics is fundamental and not a human creation.
Maybe I missed it.
Quote: gordonm888I have been reading "Quantum Philosophy" by Robert Ormes - which is concerned with this question and the reconciliation of quantum physics with the physical world that our senses reveal to us. Ormes argues pretty convincingly that mathematics is fundamental and not a human creation.
I would never wait for someone else to "save" me when it comes to the quintessentials. Besides, I had a remarkably interesting high school physics teacher who used to tell us of the text-book physics, "It's all lies."
is there really a finite 1? If there is than it would be relative to each individual person where my "1" does not necessarily equal your "1".
If I were to say "1 apple" how do you quantify that in the natural world? In that case if you grab any apple and grab any other apple from a box, you may not necessarily have exactly 2 apples, right?
I really wish i understood complex math so that I could answer my own question :(
Quote: ajemeisterI really wish i understood complex math so that I could answer my own question :(
Ideally, that's the sort of admission which ought to be "drummed into each of us" from an early age and on. Using a lot of lofty notation, etc, is no substitute for "learning how to think" about what this means while you're young enough to eventually come to profit by it.
