A Very Bready Question of Infinity and the Zeno Paradox

I know I know... just what can toast have to do with the concept of infinity??

Well quite a lot it turns out... you see when one places bread into a toaster they do so with the express intention of turning said piece of bread from bread into Toast.

In 5th Century BC a Pre-Socratic philosophy named Zeno of Elea proposed an interesting thought experiment that made one think rather hard about distance between two objects and infinity, in his case it was the distance Achilles could run to catch a tortoise that had a head start.... simply put Zeno's concept divided time and distance using infinity and stated that no matter how far Achilles had run, the tortoise would always have moved forward and so Achilles would always have to catch up...

In essence this is a bit like stating if you were to set off towards home and you did half the distance then you did half the remaining distance and you did this continually you would never reach home...

Obviously this isn't what happens... so what does all this have to to do with bread and toast??

Zeno's thought process raises a very interesting question about our doughy friend.... when does bread stop being bread and become toast? Is there a definition?

Well the chemist among us may state: -

The Maillard reaction (/maɪˈjɑr/ my-yar; French pronunciation: ​[majaʁ]) is a chemical reaction between amino acids and reducing sugars that gives browned foods their desirable flavor. Seared steaks, pan-fried dumplings, breads, and many other foods make use of the effect. It is named after French chemist Louis-Camille Maillard, who first described it in 1912 while attempting to reproduce biological protein synthesis.[1][2]

The reaction is a form of nonenzymatic browning which typically proceeds rapidly from around 140 to 165 °C (284 to 329 °F). At higher temperatures, caramelization and subsequently pyrolysis become more pronounced.

The reactive carbonyl group of the sugar reacts with the nucleophilic amino group of the amino acid, and forms a complex mixture of poorly characterized molecules responsible for a range of odors and flavors. This process is accelerated in an alkaline environment (e.g., lye applied to darken pretzels), as the amino groups (RNH3+) are deprotonated and, hence, have an increased nucleophilicity. The type of the amino acid determines the resulting flavor. This reaction is the basis of the flavoring industry. At high temperatures, acrylamide can be formed.[3]

Source: - WIKI

But even Chemistry must obey the laws of Physics....

Physics and math is my field and a simple question such as when does bread become toast have some rather interesting aspects to it that coincide with many of the subjects I get involved in. Chief among these is the transition of matter from a chaotic state into coherence.

So could the answer lie in the chemical reactions, well of course those reactions do indeed occur how many of those reactions needs to take place before we define the bread as toast??

Then is it a question of definition, that we need to count how many molecules have been modified and if more than 50% of the surface area has been modified then we should define it as toast?

This then raises the question of time.... at which point in time does bread become toast?? Well given that the smallest dividable amount of time is Planck time that is 10 to the power of -44 of a second...

So should we have a detector that could detect the percentile of molecular change across the surface of the toasting bread that could operate with a resolution of taking a frame per unit of Planck time... we should be able to tell when bread becomes toast... correct?

Theoretically it would be possible... but one must realize that the average time a normal medium sliced round of bread would turn into toast would be somewhere around 3.339170698e+45 frames.... that 33400000000000000000000000000000000000000000000 frames rounded up.... If you were to look at one frame per second... it would take you 37000 years to watch all of the footage captured...

Even so it would be possible... there is nothing in the laws of nature to prevent such an endeavor...

So to conclude.... Bread does indeed turn into toast at a definable point... but If anything I would like you take away with you that the concept of dividing Time and space is not Infinite and both time and space has a unit limit upon them that is quantifiable, but is at such a scale that at this time we are unable to do so and thus appears to be indistinguishable from being infinitely dividable from our perspective, even though our experience refutes the sense.

And!

Have more respect for your tasty bready treats!

Peace,

Korg.

a reply to: Korg Trinity

Bread turns to toast when I say it does. We all like our toast how we like it.

So it is one of those things that expresses our individuality.

So I would ask, "What does science have to do with it?" I do not need someone else telling me how I like my toast.

The answer is infinitely variable.

P

originally posted by: pheonix358
a reply to: Korg Trinity


The answer is infinitely variable.

P

Given the finite number of molecules in the bread and the finite number of people that could have such an opinion, even the aesthetics of the toast are not infinite.

I'm dumb, how can the faster guy never catch the slower guy?

a reply to: Korg Trinity

this thread made me want toast. brb.

originally posted by: Indigent
I'm dumb, how can the faster guy never catch the slower guy?

to ask the question implies you are not dumb at all...

The idea is simple. If you take a number let's say 10 and you remove 50% of it that leaves 5 right? and you then take another 50% that leaves 2.5 and you then take another 50% that leaves 1.25 and you do this continually to infinity... what you have is a circumstance whereby you never reach Zero.

The same can be said of Achilles who was trying to catch the tortoise who was ahead of him... Now of course this isn't what we experience in reality, but in Math if you apply infinity it can be shown to be true...

So why doesn't reality reflect the math.... it's because the universe is not infinite in scale, there is a point by which you can no longer divide by. a Fundamental unit of both space and time. That is what we call the Planck length. The smallest quantifiable measure of reality.

So even though we can in our minds and our maths create a mathematical model that adds up it does not reflect nature. Unfortunately this is the case with many of the mathematical models we have today that predict unobserved phenomena. Until there is observable and experimentation data to confirm it.

a reply to: Korg Trinity

I don't get it sum of (1/2)^n from 1 to infinite is 1 no matter how infinitely you divide it, it will converge

originally posted by: Indigent
a reply to: Korg Trinity

I don't get it sum of (1/2)^n from 1 to infinite is 1 no matter how infinitely you divide it, it will converge

Of course you are correct in reality... but Zeno's argument is based on the assumption that you can infinitely divide space and time. With each step Achilles takes, both the space and time is decreasing, and so dividing space and therefore time into smaller and smaller slices. It's an infinite series... meaning there is no end to it.

Before we knew about quantum mechanics or had a concept of the Planck scale... we could infer that there is absolutely a finite number by which you can divide the universe into. because if nature resembled the Achilles paradox, we the earth the sun the solar system, galaxy and all galaxies could never have existed.

Do you see?

a reply to: Korg Trinity

So reality has a frame rate known as Planck Time?

originally posted by: bigfatfurrytexan
a reply to: Korg Trinity

So reality has a frame rate known as Planck Time?

Exactly. each frame displaying at 10 to the power of -44 seconds. or 185509483244800000000000000000000000000000000000000000000 FPS to be precise.

originally posted by: bigfatfurrytexan
So reality has a frame rate known as Planck Time?

originally posted by: Korg Trinity
Exactly.

Actually this has never been confirmed.

The Planck time is a mathematical construct derived from the Planck Length, which it the shortest length we can observe without the Heisenberg Principle fuzzing out the result. The Planck Time is consequently nothing but an extension of this concept - it is how much short a period we can observe without affecting a system, not how much sort of a period that absolutely exists in a system. Quantum Mechanics does not necessarily imply that the Universe has a frame rate equal to a Planck time, or that the Universe has a frame rate in the first place for that matters.

More experimentations are needed to confirm if the Universe really is (or not) quantized at the Planck Time.

originally posted by: swanne

originally posted by: bigfatfurrytexan
So reality has a frame rate known as Planck Time?

originally posted by: Korg Trinity
Exactly.

 

Actually this has never been confirmed.

The Planck time is a mathematical construct derived from the Planck Length, which it the shortest length we can observe without the Heisenberg Principle fuzzing out the result. The Planck Time is consequently nothing but an extension of this concept - it is how much short a period we can observe without affecting a system, not how much sort of a period that absolutely exists in a system. Quantum Mechanics does not necessarily imply that the Universe has a frame rate equal to a Planck time, or that the Universe has a frame rate in the first place for that matters.

More experimentations are needed to confirm if the Universe really is (or not) quantized at the Planck Time.

For those that might want to wait for experimentally verified data on that might be waiting a long time, since the only way to probe such levels of reality are from within a simulation, and this will be the only way to directly observe anything at the Planck scale for a very very long time... We are talking about technology in order of magnitude of say what a Type 3 civilization might have access to.

But at the risk of being accused of being a hypocrite, the math does indeed add up concerning Planck Time.

a reply to: Korg Trinity

i have heard of electroncs, photons, etc being referred to as "change of state particles" in the context of reality being The Universal Wavefront (or something like that).

In that way...it sounds like a near perfect analog to a projected reality (i.e., holographic).

a reply to: Indigent

I don't get it sum of (1/2)^n from 1 to infinite is 1 no matter how infinitely you divide it, it will converge.

Zeno didn't know that.

a reply to: swanne

The Planck length is derived from the Planck constant, which does appear in the statement of the Uncertainty Principle (the Planck length and time do not)

The uncertainty in the position of an observed particle, times the uncertainty in its momentum, must have a value greater than or equal to half the Planck constant. The Planck constant is one of three constants whose product is the Planck length. The other two are the gravitational constant and the speed of light.

Pardon me for not writing the equations, I can't be bothered with the special characters necessary.

But you see, the Planck time does have a fixed value based on theory. It is simply the time taken for a photon to traverse the Planck length. It, too, is constant.

As bfft so succintly put it, reality has a frame rate.

a reply to: Korg Trinity

** i rather like PHEONIX answer, the toast is done when i decide it is and Swanne is right that everything about QM is fuzzy because the particles are too small to measure anyway, so we have to use Probabilities adjusted to match Realities. INDIGENT shows the graph which has Baffled thousands of philosophers and Math professors for 2400 years since Zeno proposed the paradox. philosophers have totally failed to explain it so far, and Oxford Uni are still churning out books on zeno. tho they should like KORG have realised that "infinity" is only a vague word meaning "some huge or small number which hasnt been defined YET (yet)". a few centuries ago the great mathematician Henry Wriothesley (1573-1624) got pissedoff with all the arguing, and invented the Concept of LIMITS to make sure that (1/2)^n came to exactly 1.0 and then spent many drunken hours in the Crown Tavern oxford with his friend William of Stratford (1564-1616). meanwhile an upstart named Newton from "the other place" (cambridge), whose grandmother had been banned from Swindlestock Tavern back in 1355 for also getting drunk too often, claimed that he was the first person to notice apples dropping off trees. this in turn pissed-off Gottfried (1646-1716) over in Leipzig, who headed to Bonn Square with gunpowder to put an end to the competition and blew up Swindlestock 1709. so you can see this problem of "infinity" got all of them into Tantrums - just like mr.Daoud (of "i am that i am" fame), who fracked the entire planet before time began, and added that he doesnt conceed Anything to ANYONE, especially no mere human.

** the story goes that Henry was struggling with a dump in the Crown Loo one day, when he noticed the particon "Flip-back Event" (FBE) of Kamanism, which had been giving him constipation in a Zen Buddhistic Trance (ZBT) for weeks. he was determined not to be Bossed around by jipper-Daoud telling him that "god" was perfect, since it was obvious "he" was a violent hebrew-miser and not perfect at all, and anyway where was Mummy god in all that theological crapp which Oxford specialises in ? undeterred by the pain of constipation, Henry was focussing on cutting an "imaginary" pair of mistress zhizhi's knickers into half, then into half again and so on, hoping he could strip her remotely by sheer will power. but something strange kept happening : every time his "image" of half a pair of knickers was cut beyond a small size which William dubbed a "Particon", Henrys bemused mind seemed to JUMP BACK onto a Falsely Expanded Fresh full-sized "Page" of image. this was very puzzling and the two drunkards put it down to the Manky Ale which had caused the Swindlestock battle in the early days when junior students like Isaac had to be banished to the swamps beyond Bedford. computers nowadays utilise "Paging" for Finite storage of course, but Henry had noticed his MIND was also doing exactly that with its FINITE "analytical work plane" (AWP) grid of Neurons which give the Meaning to "meaning" (epistem). William spent most of his time raving about Macbeth, and left Henry to get on with his "imagination" that Zhizhi's knickers would come off any minute soon, since the Mind is a FINITE mechanism /quantity of Neurons, and there is a "Particon GAP BETWEEN the neurons of the (AWP) on which any finer image details cannot (NOT) be recorded. So in effect your Observation Reflections cease, and the Mind BLINKS (Literally, you can notice it !! ), and jumps back onto the False Expansion and the seeming "endless" ability to dichotomise, and we need to FORCE a math LIMIT onto the series. QED voila "Abstract" math is JUST THAT, an abstraction from Reality, not reality itself. humans are "free" to propose penguins on mars or 10^1000 assh*les on the head of a pin (Aquinas 1225-1274), but in reality they do not exist. both Achilles and the tortoise have definite "diameters" and are OVERTAKABLE - not "infinitely"dividable, and INDIGENTS graph shows what really happens of course. but if we follow philosophers analytical method "in the time-t that it takes to move forward distance-d" etc, and converge our focus on the awaited Overtaking point, achilles can never finish his series. just like cambridge can never win any more boat races while cameron is busy destroying the economy.

** to the disgrace of "philosophers" this unrationalised situation is STILL foisted onto school math students worldwide, with NO neuronic-Web explanation for Why series must end - it all being covered up by the vague Concept of "Limits". so the Earl of southampton's famous BLINK on the Crown Loo set the course for Kamanic explanation of both the "Human Cognitive Mechanism (HCM) and the demise of "god" the self-Praising Tyrant of Pisces. very soon the Master of Aquarius will collect his righteous Lottery Winnings, rescue Summer and Dolly Zhou from the Viper moirai Daoud's grip in Jiangsu, and Our Mother Chang'e will take over Administration of this Planet of Moonchildren which has been Butchered for millennia by the psychopathic "god" / Elohim (eloah/allah) of zab-Nibiru. Needless to say that will be the end of Bankers-puppets like cameron, and we will invite Iceland to show us how to form a Democracy [ governed by WOMEN ] as well as wash out all the churches with disinfectant to get rid of all the homosexual "theologians" and paedophiles. how mal-influential some "little" words can be : the entire History of Earth strewn with Wars, chaos, confusion and Devils disguised as "god", caused by CONFLATION between the 2-dimensional Transcendental GOD of Nature [the Cognitive Background Plane (CBP) or Nothing out of which Everything AWOKE ], and the Babylonian /hebrew trinity EGO-god-EGO and holy ghost (!) that claims it "created" everything INCLUDING even Our Mother in Heaven, the only one who REALLY cares for us. could anyone get a bigger more EFFECTIVELY evil EGO than that self-Praising Butcher ? look at his great works in Syria RIGHT NOW.

ptube.pk... [ iyeoka baba ] Kaman of Elea 1972
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a reply to: Korg Trinity

I think the problem is that we are not defining toast. Once we have a definition/concept of toast, we can conceive it; and once it is conceived, as per the concept, we have toast. That is, the image of the conceptualization is toast.

Think about it like this:
formation/physicality/matrix/logos, like these words, are images of awareness/concepts (body)
awareness/concepts/interpretations/perceptions are of forces (soul)
and my will/desire/forces/pleasure is to define toast. (spirit)

So what I am doing right now is imaging/interpreting the forces/spirit within my body/the body...

my will is to define toast (spirit)
my awareness is of my will to define toast (soul and spirit)
these words are the image of my awareness of my will to define toast (body soul and spirit)

Once you have accepted that, then you can move into seeing that infinity is one thing, like my last sentence above (these words are the image of my awareness of my will to define toast - all three are one).

To better help you conceptualize it, think about it like there is only one color and it has many shades. e.g. When, after adding more pigment, or altering the force of photons, does green end and yellow begin? To answer it, you must solve for force as it is conceptualized/as it is perceived.

So, who defines toast? The force, the witness, or the physical form of the witness(the image of perception). Again, the answer is all 3.

It is like the answer to which came first: the chicken or the egg? The answer being: the chicken and the egg are one.

My body is the image of how my body's awareness interprets its forces/spirit/desire/will/its pleasure.

Define toast, when it is conceived (when your definition/concept is met), you have toast.

originally posted by: MasterKaman
a reply to: Korg Trinity

** the story goes that Henry was struggling with a dump in the Crown Loo one day,

Thank you for this contribution, it made me smile and giggle as the imagery played out within my mind... One might think that Infinity drove these people to do such things but I can assure you their actions were not only their own, but in true form for the day!

a reply to: Korg Trinity

Similar to this:

"The sorites paradox (/soʊˈraɪtiːz/;[1] sometimes translated as the paradox of the heap because in Ancient Greek: σωρίτης sōritēs means "heap")[2] is a paradox that arises from vague predicates.[3] A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? (Or are even no grains at all a heap?) If not, when did it change from a heap to a non-heap?"

en.wikipedia.org...

originally posted by: Astyanax
a reply to: Indigent

I don't get it sum of (1/2)^n from 1 to infinite is 1 no matter how infinitely you divide it, it will converge.

Zeno didn't know that.

What many people don't realise is the humans of prehistory were just as intelligent as us and in many ways forced to be far more resourceful... what they lacked was knowledge... The advance of science building upon the knowledge of the last generation growing exponentially.