Mysteries :
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my rhinestone math hat is still in the laundry this morning;

so, my coffee and i will attempt to merely wax philosophical

it is true that pi and √2 (etc.)

will appear in their exact form

(naturally slash ...automatically)

when happened upon accidentally

such as using the length of a square's diagonal for anything further

(regardless of anyone's current understanding of irrationality, etc.)

but if an irrational number is used

without being brought to naturally,

we rationally suspect foreknowledge,

wandering unarmoured into a gauntlet,

and shielded only by our calculators, but:

without consulting my notes, i can recount (like a TNG epidose)

that the poor bloke who discovered that √2 is indeed irrational

...did not end well (though history is ...divided, as to ...specifics)

the ancient greeks were convinced that, since:

there are infinite fractions between 1 and 0,

there should be no such thing as irrationals;

the fractions should account for all infinity

...ah, but there are many flavors of infinity

for instance, in our modern infinite appreciation, we now know that

if you count to infinity using only 1's, it will take you twice as long

vs counting to infinity using 2's, which gets there twice as fast

but there is no "there" to get to, it just keeps going forever...

(so, infinity is kinda only as far as your own personal horizon)

sorta like how dividing by zero, etc. produces DNE (does not exist) errors

but as a denominator approaches zero, the limit/result approaches infinity

i used to like to say "anything divided by nothing equals infinity"

(thinking myself simultaneously clever, and clever, and clever...)

but our now modern math is very careful about such dealio thingies

cuz so many things go to infinity

many roads lead in that direction

(so, the original name was sposedta be Roam... y’know, like, to “roam”?

n we were thinkin maybe: all roads could lead, like, away from there...)

as i say: coffee + vacation = qed

a curve known as Gabriel's Horn

has infinite area in 2 dimensions

(as x approaches infinity, y approaches 0)

but in 3 dimensions, the volume is pi (aha, hehe)

- probably... infinite thingies... like that... one imagines?

...anyways, using humble 22/7 (etc) in place of proud pi (etc)

easily seems like known ancient historic mere muggle attempts

...as per their limited understanding...

and our limited understanding of that

"no one expects the spanish inquisition"

Satire is a little like proof by contradiction

which first assumes a false estimate is true

and plugs that into the equation in question...

which then naturally produces erroneous results

...such as saying wanton silly things like 2 + 2 = 5

so, now we know the presumption is indeed false

and may more easily track down the actual truth

so, just because you have someone using 22/7 in place of pi

doesn't necessarily mean that they (obviously) didn't know

that proud pi wasn't equal to humble 22/7 exactly

...it may have just been more ...convenient... (hmm)

(which may have been the impetus for inventing math)

...for example; pi squared is kinda approximately 9.8

...which is also coincidentally approximately "little g"

or Earth's gravitational effect at or near the surface

9.8 meters per second squared

(or 32 feet per second squared)

my favorite math professor likes to joke

that one can be substituted for the other

which, of course, is true if you're in a hurry

and exactitude is unnecessary, such as his tests/exams

where proof of understanding is the whole/only point

(ironically, higher math sheds a need for calculators)

(...the scientific mode of the windows 10 calculator

goes out to like 20 digits past decimal or something)

in this fashion, political satire works by giving your opponent the benefit of the doubt

(let's say the world is flat, now let's see what else would have to be true... aha, hehe)

and often points out blatant hypocrisy or willful ignorance

due to the inherent hilarity of the erroneousness produced

thus, often very effective at exposing disingenuousness, etc.

(or at least saving poor saps from wandering off alleged edges)

"on second thought, let's not go to camelot, it is a silly place"

=o)

so, how does one prove anything, mathematically,

by other than a meticulous process of elimination,

using proof by contradiction, all out into ...infinity?

aha - proof by induction - hehe

(we will induce the truth from it)

to prove that some equation containing n is true for all n

- basically, you start with n=1, then plug in n+1... for fun...

if still true, we then substitute n+1 for n, giving us (n+1)+1

and usually end up with some version of the original premise

n both sides being equal, we pat our and each other's shoulders

seemingly relaxed now that we have evidence of our own cleverness

...perhaps oblivious to our own obliviousness

regarding ancient awareness of irrationality

so, if we want to prove that the ancient builders/architects...

had knowledge of the inherent irrationality of some numbers,

we just hafta catch em in the act

of actually being that irrational

'o.

everyone watch a vid

on Pascal's Triangle

so, my coffee and i will attempt to merely wax philosophical

it is true that pi and √2 (etc.)

will appear in their exact form

(naturally slash ...automatically)

when happened upon accidentally

such as using the length of a square's diagonal for anything further

(regardless of anyone's current understanding of irrationality, etc.)

but if an irrational number is used

without being brought to naturally,

we rationally suspect foreknowledge,

wandering unarmoured into a gauntlet,

and shielded only by our calculators, but:

without consulting my notes, i can recount (like a TNG epidose)

that the poor bloke who discovered that √2 is indeed irrational

...did not end well (though history is ...divided, as to ...specifics)

the ancient greeks were convinced that, since:

there are infinite fractions between 1 and 0,

there should be no such thing as irrationals;

the fractions should account for all infinity

...ah, but there are many flavors of infinity

for instance, in our modern infinite appreciation, we now know that

if you count to infinity using only 1's, it will take you twice as long

vs counting to infinity using 2's, which gets there twice as fast

but there is no "there" to get to, it just keeps going forever...

(so, infinity is kinda only as far as your own personal horizon)

sorta like how dividing by zero, etc. produces DNE (does not exist) errors

but as a denominator approaches zero, the limit/result approaches infinity

i used to like to say "anything divided by nothing equals infinity"

(thinking myself simultaneously clever, and clever, and clever...)

but our now modern math is very careful about such dealio thingies

cuz so many things go to infinity

many roads lead in that direction

(so, the original name was sposedta be Roam... y’know, like, to “roam”?

n we were thinkin maybe: all roads could lead, like, away from there...)

as i say: coffee + vacation = qed

a curve known as Gabriel's Horn

has infinite area in 2 dimensions

(as x approaches infinity, y approaches 0)

but in 3 dimensions, the volume is pi (aha, hehe)

- probably... infinite thingies... like that... one imagines?

...anyways, using humble 22/7 (etc) in place of proud pi (etc)

easily seems like known ancient historic mere muggle attempts

...as per their limited understanding...

and our limited understanding of that

"no one expects the spanish inquisition"

Satire is a little like proof by contradiction

which first assumes a false estimate is true

and plugs that into the equation in question...

which then naturally produces erroneous results

...such as saying wanton silly things like 2 + 2 = 5

so, now we know the presumption is indeed false

and may more easily track down the actual truth

so, just because you have someone using 22/7 in place of pi

doesn't necessarily mean that they (obviously) didn't know

that proud pi wasn't equal to humble 22/7 exactly

...it may have just been more ...convenient... (hmm)

(which may have been the impetus for inventing math)

...for example; pi squared is kinda approximately 9.8

...which is also coincidentally approximately "little g"

or Earth's gravitational effect at or near the surface

9.8 meters per second squared

(or 32 feet per second squared)

my favorite math professor likes to joke

that one can be substituted for the other

which, of course, is true if you're in a hurry

and exactitude is unnecessary, such as his tests/exams

where proof of understanding is the whole/only point

(ironically, higher math sheds a need for calculators)

(...the scientific mode of the windows 10 calculator

goes out to like 20 digits past decimal or something)

in this fashion, political satire works by giving your opponent the benefit of the doubt

(let's say the world is flat, now let's see what else would have to be true... aha, hehe)

and often points out blatant hypocrisy or willful ignorance

due to the inherent hilarity of the erroneousness produced

thus, often very effective at exposing disingenuousness, etc.

(or at least saving poor saps from wandering off alleged edges)

"on second thought, let's not go to camelot, it is a silly place"

=o)

so, how does one prove anything, mathematically,

by other than a meticulous process of elimination,

using proof by contradiction, all out into ...infinity?

aha - proof by induction - hehe

(we will induce the truth from it)

to prove that some equation containing n is true for all n

- basically, you start with n=1, then plug in n+1... for fun...

if still true, we then substitute n+1 for n, giving us (n+1)+1

and usually end up with some version of the original premise

n both sides being equal, we pat our and each other's shoulders

seemingly relaxed now that we have evidence of our own cleverness

...perhaps oblivious to our own obliviousness

regarding ancient awareness of irrationality

so, if we want to prove that the ancient builders/architects...

had knowledge of the inherent irrationality of some numbers,

we just hafta catch em in the act

of actually being that irrational

'o.

everyone watch a vid

on Pascal's Triangle

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