Which is it then?

You have said that I'm wrong which is different to showing that I wrong.

Again, the answer is that the number of points on a line segment is uncountable. — Banno

You are implying that:

- 1/0 is illegitimate
- 1/0 is uncountable / infinite

So which is it? It cannot be both.

You cannot make a coherent counter point. What am I to conclude? - You have no coherent counter points. If you had a coherent counter point, I'm sure you would make the effort to explain it but you don't. Your mind is closed to the possibility that what you were taught at school is wrong, yet as I've pointed out, it is a certainty that a good proportion of what you were taught at school is wrong.

Engage with my argument for F**Ks sake.

If you have a point with zero length, how many are there on a line segment length one?

1 / 0 = ?

You have failed to counter my argument and move on to a therefore completely unwarranted conclusion. That is childish and also admitting defeat.

As usual you are obnoxious and unwilling to engage with the argument.

They agree with me that the number of points in a line segment is uncountable, not undefined — Banno

How can you count something that does not exist? (if a point has zero extent, it does not exist). How can you flaunt basic mathematics. 1/0 is clearly not equal to 'uncountable'.

I guess this is the point of the thread - there are people (not just me) who disagree with the received wisdom of science and mathematics. Is it correct to dismiss/discourage them or engage with them to understand their issues?

So are you suggesting that:

1/0 <> UNDEFINED

?

You are the one not understanding the point and I concur that this conversation is serving no purpose.

what you are missing is that 1/0 is not equal to "undefined", but that mathematics, for good reason, forbids division by zero — Banno

UNDEFINED is a legitimate mathematical expression. It is perfectly valid to write 1/0=UNDEFINED. Or √-1 = UNDEFINED (in non-complex maths). Or whatever.

It matters little, however, if you squabble with my syntax, the definition of a point as having zero extend implies divide by zero whenever we wish to know how many points constitute a line segment, a plain, etc... that was my point.

See here for example:

http://mathworld.wolfram.com/Undefined.html

The following statements are equivalent:

- You should not divide by zero
- (any number)/0 = UNDEFINED

Why?

A third time: do not divide by zero — Banno

I know, that's why a write 1/0=UNDEFINED - I know it is an illegitimate operation - so I write UNDEFINED. This is the normal convention from maths.

But maths, by assuming a point has zero extent - is legitimatising division by zero - a point composes a line so you have to divide by zero to find out how many points there are on a particular line segment.

:grimace: Your problem is that you do not take sufficient time reading and understanding other people's posts. You have not addressed in any way the point I gave here:

https://thephilosophyforum.com/discussion/comment/362723

Resorting to vague generalisations, rather than addressing the point I'm making.

Why can't Devan's see that division by zero is an illegitimate act? — Banno

I know it is illegitimate; that is why I say it equates to UNDEFINED.

But the definition of a point, as having zero extents, is also equivalent to division by zero:

- You want to divide a line segment length 1 into 0.25 length chunks: 1/0.25=4
- You want to divide a line segment length 1 into 0 length chunks: 1/0=UNDEFINED

So I hope you can see the problem - the definition of a point as having zero extents enshrines into maths that division by zero can produce a defined result (∞).

It leaves one nonplussed. Devans is not stupid; but then again... — Banno

The full explanation of the point I was making is given in this post:

https://thephilosophyforum.com/discussion/comment/362723

Right, so the mathematical definition of a point is 'against the rules' ... of maths.

That is rather my point - maths with its definition of a point having zero extents - flaunts its own rules - there is an insistence in maths that both of the following are true:

1. 1/0 = UNDEFINED
2. There is an infinite number of points on a line segment length one

That equates to a belief in both of:

1. 1/0 = UNDEFINED
2. 1/0 = ∞

You see that obviously both [1] and [2] cannot hold at the same time... unless UNDEFINED = ∞ ... which is my belief.

I am not a believer in ID either, but I think the field is at least a required counter-balance to mainstream evolutionary science.

I wonder about how evolution could lead to comedy or music - neither seems to have an obvious evolutionary driver - so I think remaining open minded maybe the correct policy. For example, there are theories, as promoted in Ridley Scott's movies, that the human race may have been genetically altered by visiting aliens at sometime in the past. Hard to disprove.

Well for example I contend that because a mathematical point has length 0 therefore there are, on a line segment length 1, 1/0=UNDEFINED points, rather than an infinite number of points.

So my thinking is different from the traditional maths explanation. Please explain where I am going wrong?

And what is that misunderstanding in this case?

Could you perhaps enlighten us as to 'the way mathematics treats infinity' and how we should interpret these teachings?

For those of you interested in the real line, did you know that if you have a cube, one foot on a side, say, there are exactly the same number of points within and on the cube as there are along one edge? — John Gill

Well that would be a paradox, unless we return to the mathematical definition of a point as something with zero extents - it is logically impossible for such a think to have any existence. In each case (line, area, volume of the cube), I would contend that number of points is UNDEFINED. So it does not tell us much about reality except that mathematics (in this instance) does not reflect it.

With the definition of a point as something with non-zero extents, it all makes more sense: there would be less points on the line than the area, and less points in the area than in the volume.

And if the Axiom of Infinity disturbs you, you would be frantic if you realized the consequences of the Axiom of Choice: " Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite" — John Gill

This is somewhat above my pay grade :grin:. I stopped reading up on maths after encountering the the axiom of infinity. It does, however, strike me that if there is an infinite number of bins, then the selection process never ends - it is not possible to complete the selection process - because the selection process requires infinite time - so therefore to my layman's mind, the axiom seems false.

Imagine the dates of the years before Christ, they go:

{ ..., 5BC, 4BC, 3BC, 2BC, 1BC, 0AD }

If time is infinite, how long does this sequence extend out to the left? Well it must extend out to encompass every number. But that's plainly an impossibility - at each point in the past (10BC, 100BC, a million BC, a trillion BC) you are 0% of the way to iteration of all the numbers (because any finite number divided by infinity is zero) - so no progress can ever made towards counting 'all the numbers'.

A believe in infinite past time is therefore akin to a belief it is possible to count 'all the numbers'.

To say that we are going to intentionally create upper and lower classes using genetic engineering is obviously going to be a huge problem. Unless we engineered away any sense of morality, MANY of the smart people at the top would say the system is BS...but with some minor adjustment it could be a wonderful system (the "happy" drugs would be for those who CHOOSE to go through life that way...and then they can be assigned the "lower" jobs in society because they don't care as being happy is more important). — ZhouBoTong

Technological progress leads to the replacement of manual labour jobs by machines. Hopefully this trend will continue - we will become more and more a knowledge-based economy - and there would be more pressure on people to have intelligent, genetically engineered children. So a subclass of less gifted, natural people, might only be a transitory phase.

If you haven't watched "Gattaca"... — ZhouBoTong

Sounds interesting, I will probably take a look.

Your fingers aren't what you think they are - if they were what you think they are, that is, objects extended in space, then they would have to pass through an actual infinity of postions in order to move. So they're not objects extended in space. — Bartricks

Please explain what my fingers are if they are not 'objects extended in space'...

Time is not stuff - not a substance - for the reasons outlined, namely that if it were a stuff there would be no intrinsic difference between future, present and past and because if it was a stuff it would have to extend infinitely — Bartricks

That's not true, under the moving spotlight theory of time, 'now' is a cursor that moves down a line (or around a circle maybe), so time can be a substance and we can still differentiate between past, present and future.

I mean, try and imagine a portion of space that isn't divisible - it's impossible. — Bartricks

To divide something, you have to insert a piece of matter in-between the two parts. If space is made up of some sort of discrete mesh/grid, then it would be impossible to divide a mesh/grid node into two - the particle of matter exactly occupies one node of the mesh/grid at any time.

How many natural numbers are there? Infinite yes? Is that a problem? No. Why? Because it doesn't lead to an infinite task. — TheMadFool

There are an unlimited number of natural numbers - they go on forever in our minds - which is different from infinity - no matter how many times you add 1, you never get to a number called infinity. Only in our minds is it possible for something to 'go on forever' - if this occurred in reality, it would be akin to magic.

How many points are there on a line? Infinite yes? Is that a problem? Yes. Why? As Zeno showed Achilles can't catch up with tortoise. An infinite task.

A point has length 0, say the line segment is length 1, then the number of points on it is 1/0=UNDEFINED. It is not infinite or unbounded, it is just UNDEFINED. It's not surprising considering a point is defined to have length 0 - so cannot exist - something with all dimensions set to zero clearly does not exist - so the question can be rephrased as 'how many non-existent things can you fit on a line segment' - an answer of UNDEFINED is exactly what you'd expect.

This tells us that any ‘point-like’ particle that exists in reality must in fact have a non-zero extension in space. So any real life line segment made up of real life points must have a finite number of points on it.

I see no such problems in infinite space. What other alternative do we have if space is not infinite? Finite space, right? And the next question would be what lies beyond space? In fact infinite regress seems to be in favor of space being infinite rather than finite. — TheMadFool

The BB suggests that space maybe finite - space has been expanding at a finite rate for a finite time since the BB - so that suggests finite space (finite spacetime too). What lies beyond is pure nothing - there is no space and no time beyond the boundaries so nothing can exist.

Given that time is just a spatial dimension we have limited access to, there should be no problem in imagining time too to be infinite. — TheMadFool

But nothing can exist forever in time, so it must have a start. See for example the argument I gave in this OP:

https://thephilosophyforum.com/discussion/6218/the-universe-cannot-have-existed-forever/p1

Time - time - is not a stuff, not a dimension. Why? Because thinking of it that way means it would instantiate actual infinities. That's sufficient to establish that it is not a stuff, not a dimension. — Bartricks

If time was finite in extent and discrete, then it would be a dimension without any actual infinities. Same applies for space.

Limits, in mathematics, are calculations - tasks - that are infinite; they involve infinite steps. — Banno

Limits involve imagining an infinite number of steps which is distinct from actually performing infinite steps - actual infinity is unconstructable. See for example Thompson's Lamp paradox for the sort of nonsense results we get when performing the limit procedure out to actual infinity.

We will never, ever, be able to empirically prove spacetime is continuous, but we might be able to empirically prove it is discrete.

My contention is that something with the structure of the real line does not and could not exist in reality - maths is not reality - and we have never found anything infinitely divisible in nature. For example, how many actually infinite sets have you encountered in your life?

I find it hard to accept that, whilst I sit here typing, my fingers are passing through an actual infinity of positions.

If one rejects infinity in the large (∞ - infinite time and space), one must reject infinity in the small (1/∞ - the continuum) also.

Time is 'stuff' because:

- The physical laws of the universe are time-aware, so time must be something (IE 'stuff')
- Time has a start, so when time started something physical about the universe changed, so time must be 'stuff'

Given that spacetime is stuff, then it needs to behave like stuff and there is no stuff we are aware of that is infinitely divisible.

Spacetime also looks like a creation (see the BB) and it is not possible to create anything infinitely large or infinitely small.

But that's a tiny minority of possible numbers. The vast majority of numbers have infinite decimal places - that infinity of decimal places (=information) would be the same for the particle in a millimetre of space as for a particle in a light year of space which seems absurd to me.

If we consider the particles within space, then it has a position - which can be regarded as information. A particle in a continuum has infinite decimal places in its position - infinite information. The same kind of infinity for a light year as a millimetre of space - hence the absurdity - the larger volume should contain more information rather than equal information - this is only possible if space is discrete. So I suppose this is an argument similar to Galileo's paradox.

The same argument for space applies to time (not unexpected given spacetime) - a year should contain more information than a second.

I would also point out:

- Matter/energy turned out to be discrete; why should we expect space to be any different?
- The only satisfactory answer to Zeno's paradoxes is discrete spacetime

The reality you are aware of, perhaps. Is there nothing else? — John Gill

If space was continuous, that would lead to a light year of space having the same informational content as a millimetre of space. That's absurd, hence space is discrete.

A dimension need not be actually infinite, only potentially so — Banno

A dimension could be finite also - the dimensions on a fixed solid like a rectangle or torus are finite - and the universe may have a definite shape (in 4d spacetime). Dimensions are finite for example when you consider the surface of the earth as a 'universe'.

Our universe started expanding 14 billion years ago, suggesting that time and space dimensions are finite - there could be simply nothing beyond these boundaries - no time and space - so no measurement beyond these boundaries is possible/valid.

Thanls Athena! I should of probably linked to a picture, here is one:



(credit: https://steemit.com/physics/@procrastilearner/intuitive-special-relativity-time-dilation)

Obviously the static clock is on the left and the moving clock on the right.

13 represents the dynamic of movement present in everything and by which everything is ever-changing and at the same time vivified by the universal force of Hunab Ku". "Hunab Ku. The One Giver of Movement and Measure. The principle of intelligent energy that pervades the entire universe, animate or inanimate — Athena

Sounds a bit like panpsychism - which maybe a possible explanation for the prime mover. I however don't believe everything can be ever changing - perpetual motion is impossible. But the universe itself may have a timeless element that is in some way intelligent and is responsible for time and the movement we see around us.

Eternal: without beginning and end. — sandman

Time seems to be more than just a concept of the human imagination - it is something concrete and real (see SR/GR) - and something concrete without a beginning (or end) is an impossibility. See for example the argument here: https://thephilosophyforum.com/discussion/comment/360708

Neither Aquinas nor any other human has any concepts to understand eternal or infinite. — sandman

The fact that it is impossible to imagine actual infinity is not IMO indicative that it is beyond comprehension, merely indicative that it is an illogical/impossible concept. For example, other things I struggle to comprehend are talking trees and square circles - but they are not beyond comprehension - they are just impossible ideas. Actual infinity is unconstructible, unmeasurable, unfathomable and leads to logical paradoxes (which are a form of Reductio ad absurdum). That is enough evidence for me that it cannot exist.

You are not coming over as snarky - getting to the truth of the matter is what's important.

..the educated may CHOOSE to not have kids — ZhouBoTong

If this continues to be the case, then it seems to fall to government to ensure the continued successful evolution of the species - a government sponsored program to produce genetically enhanced, super intelligent, offspring maybe required. That may sound quite like Brave New World, but then I did not find that book to be a completely dystopian view of the future.

I have not read 'Island', the utopian counterpart of Brave New World, but I understand it introduces the concept of mutual adoption clubs (MACs) - formed of fifteen to twenty-five couples. This is the type of approach that might be required in combination with genetic engineering. I believe the MAC approach would result in a lessor impingement of personal freedom - through the economies of scale applied to child rearing - than the traditional 2 parent family approach, so the better educated in society would be more attracted to it.

but we would have to ban "natural" births to prevent the "negative" genes from being passed — ZhouBoTong

Yes that might be a step too far. As you point out, the natural born community could get left behind by the genetically altered community. I think however, both the natural and genetic communities would speak the same language and I am only really advocating genetic engineering for increased intelligence, not extra limbs or anything like that. I think it would be an extension of situation we have today, people with IQs ranging from 50 to 250 all live in the same community, it is just there would be a concentration of genetically altered folks at the high end of the spectrum.

Nevertheless, some components of our knowledge are more stable than others. — Pantagruel

Agreed. The percentage of our knowledge that is sound/stable increases with time. But I don't quite think that percentage is currently high enough to abandon critical thinking.

I'm of the opinion that people should not be discouraged from posting articles critical of science/maths just because they are not a subject matter expert:

- There are enough folks on the forum to straighten out the odd error in OPs
- It is a learning experience
- More posts mean we are more likely to come up with some good stuff

There is the zero energy universe hypothesis:

https://en.wikipedia.org/wiki/Zero-energy_universe

So the energy/matter would be created in the initial BB at the start of time.

Or, the energy/matter pre-existed the start of time (existed timelessly) and entered spacetime when time started.

I should probably have said 'the matter that constitutes the universe exists within time'. Matter can't exist forever within time and with no matter the universe would be null - leading to the requirement for something external to time to start everything off.