## "0.999... === 1" is at the very least internally consistent

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### Re: "0.999... === 1" is at the very least internally consist

"5" in "5 minutes" merely says that the period of time is composed of a finite number of things. It does not say that the period itself is finite. That depends on what the word "minute" means. If a period of time we call "minute" is composed of an infinite number of moments, then "5 minutes" is composed of an infinite number of moments too -- in spite of the fact a finite number is used in its description. Basically, if something is described as being composed of a finite number of things, it does not necessarily mean it is a finite thing itself. It depends on whether the things it is composed of are themselves finite or infinite. As an example, "5 infinite queues of people" is an infinite thing in spite of the fact it's described using a finite number.

The thing is that, if you say that "minute" is infinitely divisible, it logically follows it is an infinite thing (since only something composeod of an infinite number of things can be infinitely divisible i.e. be able to be divided into an infinite number of things.)

If an infinitely divisible period of time can be free from atomic (i.e. indivisible) parts, can you describe such a period of time? What is it composed of? "Well, a minute is composed of 60 seconds." Cool, you're saying a minute is a collection of things -- these things being seconds. But are these seconds things-in-themselves or are they collections just as well? "Well, a second is a collection too. It's a collection of 1,000 milliseconds. And milliseconds themselves are collections too, being composed of collections that are composed of other collections and so on without an end." But in order for a collection/set to be something rather than nothing, it must have more than one element. If it does not, if it's just a collection of collections of collections and so on, then it's nothing at all.
Magnus Anderson
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:"5" in "5 minutes" merely says that the period of time is composed of a finite number of things. It does not say that the period itself is finite.
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The thing is that, if you say that "minute" is infinitely divisible, it logically follows it is an infinite thing (since only something composeod of an infinite number of things can be infinitely divisible i.e. be able to be divided into an infinite number of things.)

I don't think any of that makes sense.

Something being infinite merely means that it is endless. It is not a reference to size unless used as "infinitely large" or "infinitely small".

When we say "infinitely divisible" - we are saying that the process of dividing can be endless/infinite (if we choose to proceed) - it has nothing to do with the size of what is being divided or whether parts are involved at all.

Magnus Anderson wrote:If an infinitely divisible period of time can be free from atomic (i.e. indivisible) parts, can you describe such a period of time? What is it composed of?

Time is always merely relative. It isn't "composed" of anything. It is a measure of how fast one thing is changing relative to another - no parts - no particles - pieces - just comparison between two rates of change.

It isn't the physics - it is the language.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:Something being infinite merely means that it is endless. It is not a reference to size unless used as "infinitely large" or "infinitely small".

It's logically implied. It does not have to be explicitly stated. It's similar to how saying that someone is a woman logically implies that that person can give birth. You don't have to state it explicitly. Saying that a queue of people is infinite logically implies that the number of people in that queue is greater than the number of people in any queue consisting of a finite number of people. Try to come up with a queue of people that is infinite and at the same time consisting of a number of people that is an integer. You can't, can't you?

When we say "infinitely divisible" - we are saying that the process of dividing can be endless/infinite (if we choose to proceed) - it has nothing to do with the size of what is being divided or whether parts are involved at all.

Yes, it means that the process of division can be endless / infinite. But if the thing you're dividing is not composed of an infinite number of parts, then no such process can take place. (Of course, it can take place in one's imagination but that's not what we're talking about here.) Can you take a collection of 5 indivisible things and divide it / split it into an infinite number of equally sized non-zero parts? You can't, right?

Time is always merely relative. It isn't "composed" of anything. It is a measure of how fast one thing is changing relative to another - no parts - no particles - pieces - just comparison between two rates of change.

It isn't the physics - it is the language.

Yes, it's language, not physics. That's what this thread is all about. I keep saying that (: And in English language, hours are composed of 60 minutes, minutes of 60 seconds, seconds of 1,000 milliseconds and so on. So when you say "Time isn't composed of anything", you're not speaking English language. My guess is that you're speaking a new version of English language invented by scientists as a consequence of their inability (or impatience?) to work with highly abstract concepts. They have to turn every highly abstract concept into something concrete. So time, according to them, is merely "what clocks show". Clocks are physical objects that you can touch, so "what clocks show" is quite material / physical. That makes their dicks hard. So when someone asks "What time is it now?", the answer is "It depends because different clocks show different things. What clock are you talking about? Jimmy's clock says it's 5AM and mine says it's 3PM. Other clocks might be showing different things." Best case scenario, this is merely a relativistic way of talking about things, not necessarily incorrect, and possibly useful in some ways, but in no way, shape or form does that imply that the alternative way of speaking about things, which is the non-relativistic way, is incorrect or otherwise inadequate.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:if the thing you're dividing is not composed of an infinite number of parts, then no such process can take place.[/quote (Of course, it can take place in one's imagination but that's not what we're talking about here.) Can you take a collection of 5 indivisible things and divide it / split it into an infinite number of equally sized non-zero parts? You can't, right?
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I keep saying that (: And in English language, hours are composed of 60 minutes, minutes of 60 seconds, seconds of 1,000 milliseconds and so on. So when you say "Time isn't composed of anything", you're not speaking English language.

I can't agree with any of that.

Magnus Anderson wrote:But if the thing you're dividing is not composed of an infinite number of parts, then no such process can take place.

That is where I am sure your thinking has failed.

Magnus Anderson wrote:They have to turn every highly abstract concept into something concrete. So time, according to them, is merely "what clocks show".

That is a different matter - I can agree with you on that one.

The universe CANNOT be composed of quanta parts (e.g. circles could not exist). And that means the substance of the universe must be infinitely divisible. There are no parts involved until mass particles form (infinitely larger than smaller portions of energy.

The existence of infinitely small portions of a substance does not mean that the substance is infinitely large in size. It merely means that whatever size it is - it could be endlessly divided without running out of that substance - there is no zero.

An infinite (endless) quantity of an infinitely (endlessly) small substance can be (almost always is) a finite (not endless) clump of that substance. Infinity reaches in both directions of larger and smaller - "infinitely larger than" or "infinitely smaller than" - but it is always larger or smaller than something finite (something not being endless - having a beginning and an end - usually beginning with zero).
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:But if the thing you're dividing is not composed of an infinite number of parts, then no such process can take place.

obsrvr524 wrote:That is where I am sure your thinking has failed.

How exactly can you take a thing that is not composed of an infinite number of parts and split it into an infinite number of parts?

Can you show a conceptual example?

I think you said earlier something along the lines of "1 / infinity = infinitesimal". That's not a good example because "1" in mathematics does not mean "a thing made out of no more than one part" but rather "a single thing, regardless of how many parts it is made out of". You can use it to quantify both finite and infinite things. You can use it to quantify finite queues of people ("one finite queue of people") but you can also use it to quantify infinite queues ("one infinite queue of people".) Obviously, one finite queue of people cannot be divided into an infinite number of groups of people; but you can infinitely divide an infinite queue of people. In mathematics, 1 is divisible by infinity merely because it is presumed that 1 is quantifying something that is actually infinitely divisible. Thus, you can't use "1 / infinity = infinitesimal" as a proof that a finite thing can be divided into an infinite number of parts. It cannot be done.

The universe CANNOT be composed of quanta parts (e.g. circles could not exist). And that means the substance of the universe must be infinitely divisible.

The only problem is that if something isn't made out of indivisible elements, it's nothing at all. The universe, thus, must be made out of indivisible elements. But that does not mean the universe isn't infinitely divisible. "Infinitely divisible" merely means "can be divided into an infinite number of parts". Think of a set of natural numbers. It consists of an infinite number of elements that themselves aren't collections of elements (and are thus indivisible.) And yet, it can be divided into an infinite number of equally sized sets of elements. $$\{1, 2, 3, \dotso\}$$ can be, for example, split into $$\{1, 2\}$$, $$\{3, 4\}$$, $$\{5, 6\}$$ and so on. It's infinitely divisible in spite of the fact it consists of indivisible elements.

The existence of infinitely small portions of a substance does not mean that the substance is infinitely large in size.

Not sure why that's important but if a thing is made out of parts that are infinitely small compared to it then the thing itself is infinitely large compared to those parts.

An infinite (endless) quantity of an infinitely (endlessly) small substance can be (almost always is) a finite (not endless) clump of that substance.

An infinite number of things (which are, by implication, infinitely small compared to the entire collection) is an infinite object that can be described using a finite number. The fact you can describe it using a finite number DOES NOT mean it's a finite thing. I think this is where the confusion lies.

The size of $$\{1, 2, 3, \dotso\}$$ can be described as "2 times the size of the set of even natural numbers". The fact we can describe its size using a finite number DOES NOT mean its size is finite. It isn't.
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### Re: "0.999... === 1" is at the very least internally consist

Prolly stupid question, but what does it mean for a circle to “exist”? Obsrvr… that a perfect circle cannot “exist” is no argument against (say) planck quanta.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:How exactly can you take a thing that is not composed of an infinite number of parts and split it into an infinite number of parts?

If the substance you are talking about isn't made of parts there is no choice but for it to be infinitely divisible. And if something IS made of parts - what lies between the parts? You cannot fill space with any shaped part other than a cube. What happens when you go diagonally across a cube? - you get a fractional quantum cube distance. Space has to be filled by some kind of distance at any chosen angle or curve (regardless of what the substance might be) and you couldn't have fractions of quanta.

Angles and curves totally destroy the idea of quantumized distance.

Ichthus77 wrote:Prolly stupid question, but what does it mean for a circle to “exist”? Obsrvr… that a perfect circle cannot “exist” is no argument against (say) planck quanta.

The diameter of a circle chosen to be a rational number distance always yields an irrational (in fact transfinite) distance for its circumference - and visa versa.

If distance itself is quantized no circumference (with a rational diameter) could ever be completed because that would require a fractional quantum distance. Or if the circumference is forced to be a rational (countable quanta) distance - the diameter could not reach across the circle - again requiring a fractional quantum distance. Circles would be an impossible concept and certainly could not physically exist.

I suspect nearly all curved shapes would be impossible.

Magnus Anderson wrote:The only problem is that if something isn't made out of indivisible elements, it's nothing at all.

Is that in the Bible? Where did you get that thought? What would the indivisible elements be made of?

Magnus Anderson wrote:I think you said earlier something along the lines of "1 / infinity = infinitesimal".

That is just a language thing - defining words for later use - not necessarily related to physical reality.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:If the substance you are talking about isn't made of parts there is no choice but for it to be infinitely divisible.

If it isn't made of parts, it doesn't exist. For a thing to exist, it must be composed of at least one part -- itself. If it's composed of no more than one part, it's indivisible. To divide a thing is to separate its parts. If there are no parts, nothing can be separated. If there is only one part, then there is no other part to separate that part from. You need at least two parts for division to take place.

And if something IS made of parts - what lies between the parts?

The answer to that question is "It depends". There is no universal answer because the answer depends on what kind of thing we're talking about. It depends on how it is defined. There may be something in between the parts (parts of other things or other parts of itself) but there may also be nothing at all.

You cannot fill space with any shaped part other than a cube. What happens when you go diagonally across a cube? - you get a fractional quantum cube distance. Space has to be filled by some kind of distance at any chosen angle or curve (regardless of what the substance might be) and you couldn't have fractions of quanta.

You seem to be talking about three dimensional space where each place within that space has no more and no less than 6 places that are immediately adjacent to it (or, in the case of infinitely divisible space, 6 places that are equally adjacent to it, given that there are no immediately adjacent points within infinitely divisible space.) The kind of shape that can fill a single place within such a space is that of a cube. And the object that can fill it can be called "atomic cube".

Of course, within such a space, nothing can move diagonally. One can only move forward, backward, upward, downward, to the left or to the right. There are exactly 6 angles of movement. An illusion of diagonal movement can be created by say making a sufficiently small step to the right, followed by a sufficiently small step upwards, followed by a sufficiently small step to the right and so on. That would be a diagonal movement towards the upper-right corner of the universe. If these steps are small enough, and if we're looking from a sufficient distance, it would appear as if we're moving diagonally. That would be pseudo- or quasi-diagonal movement. Perhaps that's precisely what's happening in our universe -- but it doesn't have to be the case. It doesn't have to be the case because atoms are not logically constrained to being cubes. They can also be spheres. If they are spheres, then real diagonal, as well as circular, movement is possible (though not necessarily occurring in reality.)

Angles and curves totally destroy the idea of quantumized distance.

Only if you believe that real curves -- and not merely quasi-curves -- exist (or can exist.) And even if they do (or can) exist, that would merely destroy the idea that spatial points have 6 immediate connections (i.e. that spatial points are cubes.) I never claimed such. I don't think anything I said implies it.

Is that in the Bible? Where did you get that thought? What would the indivisible elements be made of?

It's not in the Bible. It's in the Book of Logic. Sets must contain things that aren't merely subsets in order for them to be non-empty sets. An empty set, as you know, is nothing. If a set is made out of subsets, and there are no elements in it, then it's an empty set i.e. nothing at all.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
And if something IS made of parts - what lies between the parts?

The answer to that question is "It depends". There is no universal answer because the answer depends on what kind of thing we're talking about. It depends on how it is defined. There may be something in between the parts (parts of other things or other parts of itself) but there may also be nothing at all.

According to you - if it is made of "nothing at all" - it doesn't exist. And if the smallest of something doesn't exist - that thing doesn't exist.

Magnus Anderson wrote:
You cannot fill space with any shaped part other than a cube. What happens when you go diagonally across a cube? - you get a fractional quantum cube distance. Space has to be filled by some kind of distance at any chosen angle or curve (regardless of what the substance might be) and you couldn't have fractions of quanta.

You seem to be talking about three dimensional space where each place within that space has no more and no less than 6 places that are immediately adjacent to it (or, in the case of infinitely divisible space, 6 places that are equally adjacent to it, given that there are no immediately adjacent points within infinitely divisible space.)

So what are You talking about instead?

Magnus Anderson wrote:The kind of shape that can fill a single place within such a space is that of a cube. And the object that can fill it can be called "atomic cube".

You seem to be missing the point.

If distance is quantized - the entire universe must be made of quantum cube distances (regardless of what substance is involved). But a quantum "atomic cube" has a diagonal - a diagonal that is not of the quantum length but rather a fractional portion. Quantum existence does not allow for fractional quantum lengths (else it wouldn't be quantum).

Of course, within such a space, nothing can move diagonally. One can only move forward, backward, upward, downward, to the left or to the right. [/quote]
You couldn't move but also the diagonals could not exist at all.

Magnus Anderson wrote:An illusion of diagonal movement can be created by say making a sufficiently small step to the right, followed by a sufficiently small step upwards, followed by a sufficiently small step to the right and so on.

And if you did that - and each step was 1 quantum unit - what distance from origin would you have traveled? How many quanta straight distance from origin? - a fractional amount.

Magnus Anderson wrote:
Is that in the Bible? Where did you get that thought? What would the indivisible elements be made of?

It's not in the Bible. It's in the Book of Logic.

Really? Give me chapter and verse. Your set logic doesn't apply.

Magnus Anderson wrote: Sets must contain things that aren't merely subsets in order for them to be non-empty sets. An empty set, as you know, is nothing. If a set is made out of subsets, and there are no elements in it, then it's an empty set i.e. nothing at all.

The universe doesn't care about sets. You are presupposing that everything is sets of parts in order to prove that everything is sets of parts.

When it comes to the circles and diagonals - regardless of what path is taken to get from one point to another - the distance from origin to destination still must exist.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:If distance is quantized - the entire universe must be made of quantum cube distances (regardless of what substance is involved). But a quantum "atomic cube" has a diagonal - a diagonal that is not of the quantum length but rather a fractional portion. Quantum existence does not allow for fractional quantum lengths (else it wouldn't be quantum).

A distance between two points refers to the length of one of the paths that connect the two points (typically the shortest path.) A path is merely a way of moving from one point to another. Commonly, one can move from one point to another point in a number of ways (hence multiple paths.) The length of a path is merely how many points there are within it. What kind of paths exist within the above mentioned type of space? Are there diagonal paths? There are no diagonal paths, right? And that means there are no diagonals at all. There are really only staircases that look like diagonals. And the length of these staircases has no fractional part.

I think you missed the bit where I said that I never said, and that I don't think I ever implied, that atoms are cubes.

You couldn't move but also the diagonals could not exist at all.

Right.

And if you did that - and each step was 1 quantum unit - what distance from origin would you have traveled? How many quanta straight distance from origin? - a fractional amount.

First step would be 1 quantum unit travelled. Second would be 2. Third would be 3. And so on. If it took me 10 such steps to reach my destination, the distance travelled would be 10 quantum units. But of course, the crossed path wouldn't be a straight diagonal.

The universe doesn't care about sets. You are presupposing that everything is sets of parts in order to prove that everything is sets of parts.

The universe doesn't care about anything because it is not a sentient being. It is us who care about things. And we care about sets because it's relevant to the subject at hand.

And yes, everything is a set. Even a single indivisible element is a set (a singleton set.) Even nothingness is a set (an empty set.) The issue here is that you're claiming that time is not composed of elements (which at worst means that it is nothing at all and at best that it is a singleton set containing only one element -- itself) and at the same time that time is infinitely divisible (which is impossible if time is a singleton set.) It's an analysis of your claim and a statement that it contains a contradiction.
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### Re: "0.999... === 1" is at the very least internally consist

One is a QUANTITY. It is 1 shoe, or 1 house, or 1 day.

1 shoe is not made of 2 1/2 shoes, and at the same time 4 1/4 shoes, and at the same time 100 1/100 shoes.

What you are claiming is that 1 shoe is made up of anything you want it to be, and all of the possibilities of quantity-fractions at the same time.

You are claiming that 1 shoe is comprised of 2 x .5 and 4 x .25 and 8 x .125 all at the same time.

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### Re: "0.999... === 1" is at the very least internally consist

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This discussion has become completely absurd.

So do you believe that light traveling straight for 1 unit then reflected 90 degrees for 1 unit reaches it's destination at the same time as light traveling from the origin directly to that same end point?

And if the universe is made of cubic distances - which direction is straight UP?
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

Motor Daddy wrote:One is a QUANTITY. It is 1 shoe, or 1 house, or 1 day.

True.

1 shoe is not made of 2 1/2 shoes, and at the same time 4 1/4 shoes, and at the same time 100 1/100 shoes.

Depends on how many parts a single shoe is composed of. If a single shoe is composed of 1,000 atomic parts, then it has halves (each half having 500 atomic parts) which means it can be described as "2 1/2 shoes". In that case, it also has quarters (each quarter having 250 atomic parts) and hundredths (each hundredth having 10 atomic parts) which means it can also be described as "4 1/4 shoes" and "100 1/100 shoes". These descriptions aren't mutually exclusive, so you can't say "It can't be all of those things all at the same time, it can only be one of those things".

What you are claiming is that 1 shoe is made up of anything you want it to be

Not really.
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:So do you believe that light traveling straight for 1 unit then reflected 90 degrees for 1 unit reaches it's destination at the same time as light traveling from the origin directly to that same end point?

If it is moving at the same speed, the asnwer is "No". And that's because the diagonal path is shorter than the other path. But how exactly is that relevant?

The point is that there are no diagonals within the type of space we've been talking about. There are 6 directions of movement: front, back, up, down, left and right. There are no top-right, top-left, bottom-right, bottom-left, etc directions of movement. There are no diagonals. So it makes no sense to ask "What's the length of a diagonal path within such a space?" Given that they do not exist, their lengths can't be equal to "a number of atomic lengths plus a fraction of an atomic length".

You can talk about a different type of space where diagonals do exist. For example, you can talk about a type of space where there is an additional direction of movement e.g. a top-right direction of movement. In that sort of space, each place has 7 immediately (or equally) adjacent places: one in front of it, one behind it, one to the left of it, one to the right of it, one above it, one below it and one that is above and to the right of it. Assuming that we're talking about a finitely divisible space, the distance between any point within that space and its 7th neighbour (the one located above and to the right side of it) is equal to exactly one atomic length. No fractional part whatsoever.

And if the universe is made of cubic distances - which direction is straight UP?

What's UP and what's DOWN is an arbitrary choice -- a matter of convention.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
obsrvr524 wrote:So do you believe that light traveling straight for 1 unit then reflected 90 degrees for 1 unit reaches it's destination at the same time as light traveling from the origin directly to that same end point?

If it is moving at the same speed, the asnwer is "No". And that's because the diagonal path is shorter than the other path. But how exactly is that relevant?

The point is that there are no diagonals within the type of space we've been talking about.

It is relevant because your required zig-zag path to achieve a diagonal direction is exactly the same length as the simple 1 unit right plus 1 unit up. Both paths are exactly 2 units in total length. So how is it that light could go diagonally faster than straight?

Magnus Anderson wrote:You can talk about a different type of space where diagonals do exist. For example, you can talk about a type of space where there is an additional direction of movement e.g. a top-right direction of movement. In that sort of space, each place has 7 immediately (or equally) adjacent places: one in front of it, one behind it, one to the left of it, one to the right of it, one above it, one below it and one that is above and to the right of it. Assuming that we're talking about a finitely divisible space, the distance between any point within that space and its 7th neighbour (the one located above and to the right side of it) is equal to exactly one atomic length. No fractional part whatsoever.

Absurd.
If you moved to that up-right position then moved directly left - where would you be? You must exist at one of the specified points and can only move one of the specified units in one of the specified directions. But if you move up-right 1 unit then left 1 unit - the point you would have to be at - doesn't exist. You would have to disappear.

Magnus Anderson wrote:
And if the universe is made of cubic distances - which direction is straight UP?

What's UP and what's DOWN is an arbitrary choice -- a matter of convention.

And if you chose one direction and I chose another - which would have to travel the zig-zag path around the atomic cubes?
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:It is relevant because your required zig-zag path to achieve a diagonal direction is exactly the same length as the simple 1 unit right plus 1 unit up. Both paths are exactly 2 units in total length. So how is it that light could go diagonally faster than straight?

You are not making your point clear. Yes, the zig-zag path is exactly 2 units long. So what? There is no diagonal path, so nothing, not even light, can travel along it.

Absurd.
If you moved to that up-right position then moved directly left - where would you be? You must exist at one of the specified points and can only move one of the specified units in one of the specified directions. But if you move up-right 1 unit then left 1 unit - the point you would have to be at - doesn't exist. You would have to disappear.

Well, it might be the case that a finitely divisible space where each place has exactly 7 neighbouring places as described in my previous post is in fact a logical impossibility for the reasons that you outlined above. I don't know because I didn't think through it. And I am not going to do so because it's merely one out of many conceivable types of space.

Your claim is that there are logically possible spaces that are composed of indivisible elements. In order to prove that claim, you will have to prove that it holds true for every conceivable type of space. You haven't done that so far but here I am pardoning you, taking the burden myself and trying to prove that you are wrong (instead of you proving yourself to be right.)

Do you realize that the type of space that I introduced in my previous post is merely one out of many finitely divisible spaces and that not every space is finitely divisible? Proving that it is logically impossible won't automatically prove that all other finitely divisible spaces are. And it certainly won't prove that the same applies to infinitely divisible spaces. You have quite a lot of work to do, I'd say.

Do you realize that so far we've been dealing with finitely divisible types of space where each point has the same exact number of neighbouring points and that there are types of spaces where different points have different number of neighbouring points?

Think of a rectangle that is 4 atomic lengths wide and 3 atomic lengths high. Use a piece of paper and draw it. Let's say the only real points lying on that rectangle (all other being imaginary) are those that lie on its outline and those that line on one of its diagonals. Because the rectangle is 4x3 atomic lengths in size, the length of its diagonal is $$\sqrt{4^2 + 3^2}$$ which is $$\sqrt{16 + 9}$$ which is $$\sqrt{25}$$ which is $$5$$. So you have exactly 6 points lying on the diagonal. The peculiarity that is present in the previous type of space is absent in this scenario. Of course, what we have now is that only four points (the corner points) have 3 neighbouring points; all other points have 2 neighbouring points.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
obsrvr524 wrote:It is relevant because your required zig-zag path to achieve a diagonal direction is exactly the same length as the simple 1 unit right plus 1 unit up. Both paths are exactly 2 units in total length. So how is it that light could go diagonally faster than straight?

You are not making your point clear. Yes, the zig-zag path is exactly 2 units long. So what? There is no diagonal path, so nothing, not even light, can travel along it.

And that means that if the light went 100 units right then 100 units up while another light zig-zagged diagonally - they would reach the destination at the same time. So why does light seem to travel the same speed in all directions regardless of angle?

Magnus Anderson wrote:
Absurd.
If you moved to that up-right position then moved directly left - where would you be? You must exist at one of the specified points and can only move one of the specified units in one of the specified directions. But if you move up-right 1 unit then left 1 unit - the point you would have to be at - doesn't exist. You would have to disappear.

Well, it might be the case that a finitely divisible space where each place has exactly 7 neighbouring places as described in my previous post is in fact a logical impossibility for the reasons that you outlined above. I don't know because I didn't think through it. And I am not going to do so because it's merely one out of many conceivable types of space.

The same concern applies to your cube proposal. If you have a meter stick laying horizontally then raise it to a 45 degree angle - does the meter stick somehow grow extra matter so its edge can zig-zag across the diagonal distance and still read 1 meter? Or should we expect it to shrink to near half its original size?

Magnus Anderson wrote:Your claim is that there are logically possible spaces that are composed of indivisible elements.

No - I have never claimed anything about elements - or parts - or items - or pieces. I believe the universe is made of a truly pure substance - not composed of any kind of parts, elements, or pieces - merely chosen portions of whatever size you wish to consider.

Magnus Anderson wrote:In order to prove that claim, you will have to prove that it holds true for every conceivable type of space.

The circle proves that (although I have no idea what "types of space" means).

Magnus Anderson wrote:Do you realize that the type of space that I introduced in my previous post is merely one out of many finitely divisible spaces and that not every space is finitely divisible?

Do you realize that all of those thoughts were proven wrong during the Greek days? It actually isn't that hard (although in your case ---).

Magnus Anderson wrote:Proving that it is logically impossible won't automatically prove that all other finitely divisible spaces are. And it certainly won't prove that the same applies to infinitely divisible spaces. You have quite a lot of work to do, I'd say.

Again the circle proves my case - but the Greeks used triangles - such as the diagonal across a unit square being the irrational and uncountable distance of sqrt2. The Pythagoreans made a big deal of it.

And yes proving no other possibility DOES prove the infinitely divisible case to be the only option.

Magnus Anderson wrote:Do you realize that so far we've been dealing with finitely divisible types of space where each point has the same exact number of neighbouring points and that there are types of spaces where different points have different number of neighbouring points?

What I realize is that none of your fantasy proposals of varied neighbouring points make any sense. And all for the same reason.

Magnus Anderson wrote:Think of a rectangle that is 4 atomic lengths wide and 3 atomic lengths high. Use a piece of paper and draw it. Let's say the only real points lying on that rectangle (all other being imaginary) are those that lie on its outline and those that line on one of its diagonals. Because the rectangle is 4x3 atomic lengths in size, the length of its diagonal is $$\sqrt{4^2 + 3^2}$$ which is $$\sqrt{16 + 9}$$ which is $$\sqrt{25}$$ which is $$5$$. So you have exactly 6 points lying on the diagonal. The peculiarity that is present in the previous type of space is absent in this scenario. Of course, what we have now is that only four points (the corner points) have 3 neighbouring points; all other points have 2 neighbouring points.

Again - same absurdity.

If you traveled 2 of the diagonal units and then turned to go directly horizontal - where would you be? You wouldn't even be able to go straight back down to the original horizontal line.

It doesn't matter what kind of configuration you dream up. The universe is NOT made of straight segments of anything so all of your examples will always be flawed. This is in part why the squaring of the circle is so difficult - if not impossible.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

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obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

MD's Box proves that light travels in space in every direction from the point in space that it is emitted, at the same speed, independant of objects in space. In other words, if a box is in motion in space, and a light is sent from the center of the box, it is impossible for the speed of light to be the same in different directions in the box. So the measured speed of light in the box refrence frame can not be the same when measured in different directions relative to the box.

Motor Daddy
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### Re: "0.999... === 1" is at the very least internally consist

Question. Is it light that travels through spacetime, or other way around? (spacetime, not BeingTime)
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

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- A marriage of Sartre & Levinas

“ Gloria Dei est vivens homo. “
Trans.: The glory of God is man fully alive.
- Irenaeus

Ichthus77
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:
Magnus Anderson wrote:
Absurd.
If you moved to that up-right position then moved directly left - where would you be? You must exist at one of the specified points and can only move one of the specified units in one of the specified directions. But if you move up-right 1 unit then left 1 unit - the point you would have to be at - doesn't exist. You would have to disappear.

Well, it might be the case that a finitely divisible space where each place has exactly 7 neighbouring places as described in my previous post is in fact a logical impossibility for the reasons that you outlined above. I don't know because I didn't think through it. And I am not going to do so because it's merely one out of many conceivable types of space.

The same concern applies to your cube proposal. If you have a meter stick laying horizontally then raise it to a 45 degree angle - does the meter stick somehow grow extra matter so its edge can zig-zag across the diagonal distance and still read 1 meter? Or should we expect it to shrink to near half its original size?

.707... of it's original size, or sqrt(2) / 2

If you have a stick of length 2, and turn it 45deg, and his way of thinking applies, then the stick is now a zigzag triangle with 1 side length 1, another side length 1, and the lenght of the stick is now the hypotenuse of that triangle.

Sqrt(1^2 + 1^2) = sqrt(2)

So a stick of length 2 changes to length sqrt(2) at 45degrees.

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### Re: "0.999... === 1" is at the very least internally consist

Found this stackoverflow answer on this topic

https://physics.stackexchange.com/a/282877/73404

and this wikipedia page

https://en.wikipedia.org/wiki/Weyl%27s_tile_argument

Flannel Jesus
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### Re: "0.999... === 1" is at the very least internally consist

Roads.png (1.56 KiB) Viewed 214 times

I have an electric car, which always travels at a constant speed of 1 unit of distance per minute. I want to get from point A to point B. There are two routes I can choose from, either travel the two roads that each have a unit of distance 1 unit, or travel the 1 road that has a unit of distance 1.4142 units.

If I choose to travel the two roads then it takes 2 minutes to get from point A to point B.
If I choose to travel the 1 road then it takes 1.4142 minutes to get from point A to point B.

Those are the facts!

Motor Daddy
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### Re: "0.999... === 1" is at the very least internally consist

Ichthus77 wrote:Question. Is it light that travels through spacetime, or other way around? (spacetime, not BeingTime)

Light travels a distance over a duration of time in space.

Space is the infinite volume of existence, irrespective of objects. Space is infinite distance in every direction.

There is 1 gallon of space in a 1 gallon gas can, regardless of how much gas is in the can. The can has a 3 dimensional distance (volume) irrespective of the gas, and that space is measured as 3 dimensional distance.

"Space" has no borders, it continues in every direction infinitely. Light travels in that space a distance per duration of time. Light travel time defines the unit of distance "Meter."

If light travels in space for 1/299,792,458 of a second the distance it traveled is 1 meter.

Objects in relative motion to space will not measure the light to travel that 1 meter compared to their reference frame, because they are in motion in space.

Motor Daddy
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### Re: "0.999... === 1" is at the very least internally consist

Motor Daddy wrote:Objects in relative motion to space ...

Are you another James S Saint follower?

Flannel Jesus
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### Re: "0.999... === 1" is at the very least internally consist

MD (not MA), space is something irremovable from objects & vice versa. Light is energy & determines time, so for it time stops, no? Then, too, motion. Is it not spacetime that moves relative to light? Is the speed of light not actually the speed of spacetime?
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

“ Gloria Dei est vivens homo. “
Trans.: The glory of God is man fully alive.
- Irenaeus

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