Cantors Paradise The infinity on earth

cantor’s paradise

zermalofrankel set theory a left numbers

the actual infinity you might be

wondering what

madness drove the 17 year old kid to

spend his entire christmas holiday

studying and researching the

mathematical nature of the actual

infinity

well the answer is actually quite simple

when i was preparing for this ted talk

the first thing i did was go onto the

tedx website and see

well what topics could i talk about well

as a christian and

someone who’s quite interested in

philosophy i thought well wouldn’t this

be a great opportunity to present some

philosophical arguments for these ex

the existence of god or perhaps i could

use this time

to prepare a powerful case for the

historical resurrection

yet the moment i looked at the rules the

first thing i saw

was well no religious or political

agenda so

while that had to go out of the window

then i thought okay i know a bit of

science how about talking about

evolution

and young earth creationism and how

they’re kind of there’s some problems

here

but then i then saw another thing

no bad science so well that had to go

out to the window as well

so i was left with nothing but the

actual infinity

and it’s not that i’m complaining about

it because it turns out the actual

infinity

is actually a very interesting topic no

pun intended there

and you might think well i’m just paid

by a math teacher to tell you

oh maths is very fun now let’s all apply

for maths

for a levels but no the actual infinity

is actually a very

interesting and profound topic that has

significant implications on

our physical world and also the

conceptual world of platonic realism

and conceptual realism so what i would

like to do here

since this topic the actual infinity is

a massive topic

i like to discuss its implications on

the physical world

and discuss whether it can actually be

applied to the physical world

whether an actually infinite amount of

things or

quantities can be realized or actualized

in our world around us both in this

temporal space

and also a spatial sense can the past be

actually infinite

and can space as a whole be actually

infinite

to discuss this i would like to turn to

the use of paradoxes

the use of paradoxes has been used

throughout the history of philosophy

to discuss or show that something cannot

happen or

that some result or some argument leads

to contradictory results

a good example of this would be zeno’s

paradoxes which is one of the arguments

i’ll be raising today

and also grim reaper’s paradox which

i’ll be also discussing in this video

so without further ado let’s get started

what is the xenos paradox

well zeno actually raises multiple

paradoxes throughout his life

which are recorded by aristotle in his

book physics

while we don’t have any direct works

from zeno we do

see a lot of his paradoxes in

aristotle’s books including

the dichotomy paradox which we’ll be

discussing in this video arcolas and the

tortoise

the stadium paradox and the arrow

paradox and others

so what is the dichotomy paradox while

there’s more responses to this paradox

i think that i love this paradox i think

it’s very interesting because of its

numerous variations not only do you have

to accept

the first paradox that zeno raises you

can also

discuss and develop it further to suit

your needs and that’s essentially what i

do

so before we get started or before we

delve deeper into these second or third

variations

i would like to discuss what the xenos

paradox is

and what idea it is trying to get at so

zeno’s paradox is best

represented by an analogy while zeno

uses a runner

i like to use a painter since i

coincidentally have a painting right

behind me

and i’m not in a museum of modern arts

i’m just in my dining room

so imagine there’s this painting a

painter is trying to draw a paint

painting well that’s what painters do so

in order to draw half the painting

you first have to draw a quarter of the

painting and before you could draw a

quarter of it

that’s to draw an eighth of its so on

add infinitum so as you can see

there there’s this potentially or this

divisions you could potentially divide

this so on

add infinitum towards the side you’re

starting to draw from

so you have half a quarter an eighth

and so on and for this infinite series i

would be saying

i’ll be referring to it as the zed

series because that would just be easier

named after a zeno so as you can see

this goes for

running for any action as well

before you move the entire thing you

have to move half of it and the z series

so what xeno tries to say that it’s

impossible for anyone to move

because in order to move they first have

to cross an actually infinite number of

series which is impossible so what are

some

preliminary responses to this argument

well the most normal one or the most

common one

is raised by aristotle in his book the

physics he basically writes

that this series is only a potential

infinite and not an actually infinite

series

however this is wrong because if you

look at the nature of the potential

infinite and the nature of the actual

infinite

what we do see is that while the

potential infinite is basically a number

or a series of numbers

going up one two three four five six or

any series like that

add infinitum the actually infinite

series

is an actually definite set of numbers

while

some of these actually infinite series

are denumerable and others are

non-denumerable

what we see isn’t a defined or an

actually infinite set of numbers which

already exist as a whole

so essentially how do we know something

is a potentially infinite or is

it an actually infinite this is what we

sometimes call a one-to-one

correspondence you see

whether one set could be put into

one-to-one correspondence with another

set if they can

then they’re equal in size for example

if you have five lobes of red and five

fish

you put one loaf of bread with another

fish and then the second

bread with a second fish third fourth

third and so on like that

so you can see that five loads of bread

have the same number of the fish because

they could put

be put into one to one correspondence so

as you can see if we

put the number of divisions in a

one-to-one correspondence with the

natural numbers which as

we’ve known or cantor discusses isn’t

actually infinite series you basically

have quite an interesting result

one of the natural numbers goes to one

in the

z series two to one half

three to one quarter and so on and into

an item there’s a one to one

correspondence so what we do see

is that with these pairs the zed series

is actually

an actually infinite series and that’s

what ben ardex writes in his

book or essay infinity so we can see

that this response that this uses a

potential infinite

it doesn’t really work so what else can

someone say in response to this

well ben ardet says well let’s imagine

time itself could also be divisible in

this set series

one minute could be divisible into one

half and a half

to a quarter and so on like the z series

now with that to mind it seems that at

face value there’s enough

points on the finite time to correspond

with the points on a finite line

so time the restriction of time on this

crossing a fine infinite or a finance

line

does not actually happen because you

actually have enough time

by one to one correspondence to actually

paint the entire painting or run the

entire distance

so what can we say to this i’ll raise

variation two of the zenos paradox

imagine you have a log and a

metaphysical knife which you cut your

exact precision to whatever you want to

cut

you have log you cut half a quarter like

the z series

now assuming that bernardette’s paradox

works it does seem that you will cut

towards the entire log and in

fact finish the entire log because you

actually have enough time to cut

from one side to another but that’s

clearly absurd if we took 10

they’ll always converge towards one side

but they’ll never actually cut or cross

the line

so i don’t think ben ardex response

works here

so how would i respond to the xenos

paradoxes because

we all know that we can move i can move

finite distances

and definitely i disagree with the

conclusion of this primary

xenos paradox that movement cannot

happen so

while it’ll be fallacious to argue that

just because i don’t like the conclusion

i have

that means that i could throw away the

arguments we have to respond to the

arguments

so what’s the best response to the

arguments in my opinion the best

response to these arguments

is the idea that these these

deconstructions

or these divisibilities do not actually

go for infinity

while you might like to say you can

conceptually devise them by infinity

it doesn’t mean that there’s physically

and actually infinite number of

divisions

why well it’s actually quite simple

because

imagine we have a painting here for

those chemists out there and i’m not

saying i’m a really good chemist but

we could see that this painting is

broken down into

paint molecules and those molecules into

elements and those elements into atoms

and they could be deconstructed into

these final quantum

particles like the quartz which cannot

be further deconstructed

into further physical elements so at the

grounding of everything there’s actually

these

indivisible things which although are

conceptually divisible

are not chemical or physically divisible

so we have

each of these indivisible things so in

fact there is no

infinite thing we have to transverse

traverse but there’s actually a finite

things we have to traverse

so would that defeat zeno’s paradox if

it does why did i raise it in the first

place

well that’s because i would like to

raise the final iteration of the final

variation of

zeno’s paradox imagine you live in a

universe well we all do live in a

universe and that universe is

according to the eighth year of the time

the dynamic theory of time the idea that

past

and future are real phenomena so

when we live in an infinite theory of

time we soon realize

that if the past was actually infinite

what while we age for example

on our first birthday or the 100th

birthday or thousandth birthday if we

lived that long

the actually infinite past would stay

exactly the same the universe will

always stay the same age

despite us aging within that universe

and that is i think

well quite absurd because how could us

age in the universe

in which the universe does not

mathematically age and you might say

well where am i getting this doesn’t age

from

well if we look at the kantour’s

infinity or his arithmetic what we do

see

is that a left null and actually

infinite number plus

n or any finite number is a left null so

any finite number when added to a in

transfinite number does not actually

change so we can see that while we are

aging in a

infinite universe the infinite universe

doesn’t actually age so that does seem

to be absurd

and furthermore imagine we have an

infinite space around us an actual

infinite side

to one side and actually infinite all

around us whether

we move right or left our coordinate

will always be the same because when we

look at coordinates it’s relative to a

different point for example

uh point five seven on a

graph would just be 5 from the x and

7 from the y so what we can see

is that each points or our coordinates

are developed or based on the idea of

finite spaces

so how does bernard respond to this or

this development of the xenos paradox

well basically what we do see is that

then our debt suggests that the entire

world

although actually infinite can be

divisible into finite places there are

finite

spaces in in every part of a transfinite

plane

but then that raises a problem since we

cannot add up to infinity

it’s absurd to suggest that the entirety

of trans-finite

spaces are built out of finite parts

because if all parts of

the finite or the universe are finite

it follows logically that in totality of

the universe

is finite because if you have finite

numbers and you add to them

you will always get a finite number so

it seems that zeno’s paradox or this

final variation of xenos paradox

does seem to defeat the idea of an

actually infinite past

or an actually infinite surroundings but

what is the grim reaper’s paradox

diaries

well the grim reaper’s paradox is

essentially the idea that

imagine there’s a guy at fred i’m sorry

her name’s fred because fred well kind

of gets killed a lot in this paradox

imagine a sentence if fred’s dead

or if fred’s alive at 12 then a grim

reaper will kill him

if fred’s alive at 11 30 a grim reaper

would spawn and kill him

so as you can see what’s happening here

is that from 11 to 12

there has to be a time where the grim

reaper kills him as the z

series decreases either a half an hour

past

12 a quarter of an hour past twelve an

eighth of an hour past 12

a gram will kill him if he’s not already

dead so we have this

actually infinite series this said

series of

grim reapers spawning in to kill fred

ever since

the bell struck at 11. so

soon if we follow the series we have to

ask ourselves a few questions

well is fred alive or dead at the end of

the series well the answer is actually

quite weird

he has to be dead because if he wasn’t

dead something would have killed him

but at the same time nothing actually

had killed him because before each grim

reaper could kill him

something before him must kill fred

already so there’s actually no definite

grim reaper which kills fred

so what do we conclude from this i think

we could conclude that

it’s impossible for us to have an

actually infinite series of causes

because if there was an actually

infinite series of causes there will not

actually be any

definite explanation for anything in the

world around us or

anything at all so the series of causes

in the past

has to be finite so now that we’ve

concluded that

causation has to be finite space has to

be finer and time has to be finite

what implications do they have on the

world around us

well i wouldn’t talk too much about this

unless i violate the

rules of tedx and i will start fearing

into the religious agenda thing

but if we accept this arguments that

i’ve raised

we soon realized that we were faced with

uh croatia

or uh existence x nilo

the universe came out of nothing because

time or space cannot be

infinite and hence there must be a

beginning to space so

as the irreligious talk this is i’ll

just leave you like that

you can find your own conclusions but

we’re all faced with

a creation out of nothing i hope that

you’ve liked everything

and i hope you’ve enjoyed this ted talk

hope you found it informative

if you want to learn more about the

actual infinity feel free to do

any more research for yourself

i hope you have a good week stay safe

and thank you