Philosophy Now Forum

bahman wrote: ↑Sat Feb 27, 2021 3:44 pm

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones. To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.

My problem is the derivative is defined as a limit and in the limit, you never reach the point while we are interested in the exact derivative of the function which means that we have to set dt equal to zero which is problematic. This means that although a continuous function is plausible but we have a problem with defining the derivative or continuous motion.

Okay, I think we are on the same page. So, do you think you have found a solution?

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You used the operative word here, 'parts'.

Any time any one is looking at any 'thing' in regards to 'its' 'parts', then they will, and will 'have to', see 'discrete'. By using the word 'parts', then one can ONLY see in relation to separated 'things'.

Because absolutely EVERY thing is relative to the observer, if one is LOOKING FOR or LOOKING AT 'parts', then 'parts', or 'separation', is what they can and will ONLY SEE.

See, what actually happened, in the days of when this was being written, is those human beings did not fully recognize nor accept just how much influence and power words, themselves, have over them.

Just look at the words used here;

" If one 'divides' a 'continuous function' into 'small enough parts' you might consider them to be 'discrete jumps' ".

Now, if we want to break this down, ourselves, into smaller parts, then what can be seen is that 'if one does 'divide' ANY 'thing' into 'smaller parts', then it is NOT just a fact that they 'might' consider the 'smaller parts' to be 'discrete jumps' but an absolute FACT that they would 'HAVE TO' consider the actual 'individual and separated smaller parts' to be 'discrete jumps'. One has NO choice in or over this matter.

If one looks at 'parts', then one 'has to' see, and thus can only see, 'separated parts', 'distinction', and thus 'discrete jumps'.

This, by the way, does NOT mean that 'discrete' NOR 'discrete jumps' actually exist. This is just what this one person is seeing, and saying, there is.

'See', if one 'says' there are 'parts', then that one will 'see', separated and distinct, 'parts'. Just like when one 'says' there is 'one thing', then that one will 'see', just, 'one thing'. However, if one 'says' there is 'one thing' that can be broken down into 'parts', then what that one will 'see' is 'one thing' with separated and distinct 'parts'.

What 'you' 'say' to 'yourself' has far more influence OVER 'you', than is FULLY REALIZED when this is first read or heard. But as human beings keep evolving along this starts off gradually being realized and accepted becoming more and more exponentially realized and accepted.

The thoughts, or thinking, within a head actually has FAR MORE POWER of people than first even realized.

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones.

And 'boundaries', 'limits', or 'distinctions' do NOT actually occur, naturally, in and of themselves, other than they ONLY occur within, and from, thinking, or more correctly from the way one LOOKS and SEES.

See, there is REALLY ONLY One continuous, eternal and infinite, 'Thing'. This 'Thing' is labeled or named with, and by, the word 'Universe. However, for thee always continually evolving Universe to be able to come to understand, and thus Know thy Self, It had to become able to LOOK AT and SEE Its Self as It Truly IS. This was and can only be done by seeing and recognizing ALL of the 'parts' of Itself. Which is where the human being comes into the 'picture'.

The continually evolving 'human being' has come along, in the long line of continual evolution, itself. This human being 'thing' has evolved to become able to see 'distinction', and then able to label and name the seen 'distinctive parts', and then furthermore to even be able write these 'parts' down, with 'distinctively different names', and thus become able to also remember ALL of these human being made up separated and distinct 'parts'.

This 'making distinction' is and was just naturally what was 'needed', in order to be able to makes sense of, and thus Truly understand, thee Universe, Itself.

For thee Universe to be able to come to Know Thyself It 'needed' a species to be able to come along and just do what the labeled and named species 'human being' is evolving, and had evolved, to be able to do.

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.

The reason it can NOT be done is because it does NOT exist.

Thee Universe, Itself, is just One, solitary, eternal and infinite continually evolving, and creating, 'Thing', which can be and will soon be PROVEN to be absolutely and irrefutably True.

There is NO 'stopping' nor 'starting' ANY where. However, there is obviously the appearance of 'things' (with an 's') coming into and out of existence, which can not be overlooked nor dismissed, in order to FULLY understand ALL-OF-THIS.

Thee One Universe is just changing in shape and form, which brings with It an appearance of distinctly different 'things' (with an 's'). But this is just because of what the Universe is fundamentally made up of and because of how this ALL works.

Dimebag wrote: ↑Sat Feb 27, 2021 10:42 pm

bahman wrote: ↑Sat Feb 27, 2021 3:44 pm

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones. To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.

My problem is the derivative is defined as a limit and in the limit, you never reach the point while we are interested in the exact derivative of the function which means that we have to set dt equal to zero which is problematic. This means that although a continuous function is plausible but we have a problem with defining the derivative or continuous motion.

Okay, I think we are on the same page. So, do you think you have found a solution?

Not yet. I talked about the limit with a few mathematicians but they couldn't convince me and resolve the problem I have with the concept.

bahman wrote: ↑Sat Feb 27, 2021 3:37 pm

Age wrote: ↑Sat Feb 27, 2021 2:48 am

bahman wrote: ↑Sat Feb 27, 2021 1:11 am
All I am saying is that 0/0 has a problem.

0/0, itself, does NOT have 'a problem'.

ONLY 'you', human beings, make and created 'problems'. Thus, it is ONLY 'you', human beings, who have 'a problem', here.

0/0 has a problem since it could be any value as it is illustrated in another thread.

So what?

'you' alone have made, and thus are causing, the 'problem'. Therefore, who do you think it is up to to 'fix it'?

bahman wrote: ↑Sat Feb 27, 2021 3:37 pm

Age wrote: ↑Sat Feb 27, 2021 2:48 am

bahman wrote: ↑Sat Feb 27, 2021 1:11 am It is undefined.

If 'it' is 'undefined', and 'this' causes 'you' a 'problem', a 'concern', or an 'issue', then I suggest that 'you' just go ahead and 'define' 'it'.

0/0 has a mathematical problem so I cannot assign a number to it.

I then suggest you just NOT using 0/0.

bahman wrote: ↑Sat Feb 27, 2021 3:37 pm

Age wrote: ↑Sat Feb 27, 2021 2:48 am

bahman wrote: ↑Sat Feb 27, 2021 1:11 am So velocity is not defined in the continuous limit.

This is because there is NO actual 'discrete'. Which can be and will be PROVEN True.

bahman wrote: ↑Sat Feb 27, 2021 1:11 am Please see this thread.

I saw 'that' thread.

So what is your opinion? Did you see the problem of 0/0?

What I see is you making a 'problem' when there is absolutely NO need to.

Also as someone else pointed out to you, you can not have something both moving and not actually moving at the exact same moment. Surely this is not that to hard to see and recognize, correct?

Dimebag wrote: ↑Sat Feb 27, 2021 10:42 pm

bahman wrote: ↑Sat Feb 27, 2021 3:44 pm

Dimebag wrote: ↑Sat Feb 27, 2021 1:04 pm Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones. To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.

My problem is the derivative is defined as a limit and in the limit, you never reach the point while we are interested in the exact derivative of the function which means that we have to set dt equal to zero which is problematic. This means that although a continuous function is plausible but we have a problem with defining the derivative or continuous motion.

Okay, I think we are on the same page. So, do you think you have found a solution?

Define what the alleged actual 'problem' is exactly, in words, then the 'solution' can be easily found, and given, in words.

See, explaining what the Universe IS, and how It works, in words, can be done very simply and very easily. People, however, can manipulate symbols and numbers to make things appear not workable or not achievable, mathematically, as well as workable and/or achievable, depending on how one looks at and sees things. In other words, depending on ones current BELIEFS, then this will influence how they manipulate numbers and symbols, to make things appear mathematically correct or not correct.

Age wrote: ↑Sat Feb 27, 2021 11:12 pm You used the operative word here, 'parts'.

Any time any one is looking at any 'thing' in regards to 'its' 'parts', then they will, and will 'have to', see 'discrete'. By using the word 'parts', then one can ONLY see in relation to separated 'things'.

Because absolutely EVERY thing is relative to the observer, if one is LOOKING FOR or LOOKING AT 'parts', then 'parts', or 'separation', is what they can and will ONLY SEE.

See, what actually happened, in the days of when this was being written, is those human beings did not fully recognize nor accept just how much influence and power words, themselves, have over them.

Just look at the words used here;

" If one 'divides' a 'continuous function' into 'small enough parts' you might consider them to be 'discrete jumps' ".

Now, if we want to break this down, ourselves, into smaller parts, then what can be seen is that 'if one does 'divide' ANY 'thing' into 'smaller parts', then it is NOT just a fact that they 'might' consider the 'smaller parts' to be 'discrete jumps' but an absolute FACT that they would 'HAVE TO' consider the actual 'individual and separated smaller parts' to be 'discrete jumps'. One has NO choice in or over this matter.

If one looks at 'parts', then one 'has to' see, and thus can only see, 'separated parts', 'distinction', and thus 'discrete jumps'.

This, by the way, does NOT mean that 'discrete' NOR 'discrete jumps' actually exist. This is just what this one person is seeing, and saying, there is.

'See', if one 'says' there are 'parts', then that one will 'see', separated and distinct, 'parts'. Just like when one 'says' there is 'one thing', then that one will 'see', just, 'one thing'. However, if one 'says' there is 'one thing' that can be broken down into 'parts', then what that one will 'see' is 'one thing' with separated and distinct 'parts'.

What 'you' 'say' to 'yourself' has far more influence OVER 'you', than is FULLY REALIZED when this is first read or heard. But as human beings keep evolving along this starts off gradually being realized and accepted becoming more and more exponentially realized and accepted.

The thoughts, or thinking, within a head actually has FAR MORE POWER of people than first even

I had to do a little research to realise what bahman is meaning, which is specifically in relation to the mathematics of functions (imagine a graph which plots an x and y axis, such that there is some relation between the x and y coordinates, this relationship is the function). Any function (curve on an x y axis) which varies continuously, can in theory be divided (artificially) at an infinite number of points along its curve. This is called a magnitude. Examples of magnitude are, time, distance, etc. you can divide them (artificially) infinitely. That is the nature of a continuous function. Now, the reason you would want to “limit” a function, is so you can find its derivative (the “slope” at any particular point on the curve). An example of a derivative of a continuous function is, as bahman is using, velocity, which is v = d/t, where v = velocity, d = distance travelled, and time = time the thing travelled in that distance. V is found whereby distance and time are plotted on this graph such that they covary, at any artificial point on the curve, they will have different but related values. The relation between those two variables is the velocity, which is the slope (angle) of the curve plotted by those two variables at any particular point on the curve.

But, there is a problem with trying to find this slope for a point. To find the slope, you have to use an artificial limit on a section of the curve you want to find the slope value of. So, you create a set of limits, or divisions on that curve, such that you can work out the relationship between those two values based on their difference between those two points on the curve.

When you do this, you are dividing something continuous, creating an artificial division on something which is, in reality, whole and can be divided infinitely.

As mentioned earlier, something discrete is like a point which has the SAME value throughout the whole of its division. Now, the artificially divided continuous function does NOT possess such a quality, and as such, cannot be viewed as discrete. Because you can infinitely divide a continuous function, the division is always containing some CHANGE in its slope throughout the section. This is opposite to a discrete point like coordinate, which is just that a point.

I hope you understand now WHAT bahman is attempting to prove, and why he cannot prove it.

I am not that clear still about The mathematics behind it, as I just educated myself on it over the past few days, and so bahman will occasionally go off on some mathematical prosings or transformations which are currently beyond my understanding, but, it still doesn’t change the fact that what he is attempting is not logically possible.

Bahman, I came across a source which discusses much of what you seem to be attempting, seemingly with little to no clear resolve, you may find it here:

https://plato.stanford.edu/entries/continuity/#1

Much if not most of it went over my head, but you may find it useful. But, I think you will find you are not alone in your attempts.

Dimebag wrote: ↑Sun Feb 28, 2021 12:51 am

Age wrote: ↑Sat Feb 27, 2021 11:12 pm You used the operative word here, 'parts'.

Any time any one is looking at any 'thing' in regards to 'its' 'parts', then they will, and will 'have to', see 'discrete'. By using the word 'parts', then one can ONLY see in relation to separated 'things'.

Because absolutely EVERY thing is relative to the observer, if one is LOOKING FOR or LOOKING AT 'parts', then 'parts', or 'separation', is what they can and will ONLY SEE.

See, what actually happened, in the days of when this was being written, is those human beings did not fully recognize nor accept just how much influence and power words, themselves, have over them.

Just look at the words used here;

" If one 'divides' a 'continuous function' into 'small enough parts' you might consider them to be 'discrete jumps' ".

Now, if we want to break this down, ourselves, into smaller parts, then what can be seen is that 'if one does 'divide' ANY 'thing' into 'smaller parts', then it is NOT just a fact that they 'might' consider the 'smaller parts' to be 'discrete jumps' but an absolute FACT that they would 'HAVE TO' consider the actual 'individual and separated smaller parts' to be 'discrete jumps'. One has NO choice in or over this matter.

If one looks at 'parts', then one 'has to' see, and thus can only see, 'separated parts', 'distinction', and thus 'discrete jumps'.

This, by the way, does NOT mean that 'discrete' NOR 'discrete jumps' actually exist. This is just what this one person is seeing, and saying, there is.

'See', if one 'says' there are 'parts', then that one will 'see', separated and distinct, 'parts'. Just like when one 'says' there is 'one thing', then that one will 'see', just, 'one thing'. However, if one 'says' there is 'one thing' that can be broken down into 'parts', then what that one will 'see' is 'one thing' with separated and distinct 'parts'.

What 'you' 'say' to 'yourself' has far more influence OVER 'you', than is FULLY REALIZED when this is first read or heard. But as human beings keep evolving along this starts off gradually being realized and accepted becoming more and more exponentially realized and accepted.

The thoughts, or thinking, within a head actually has FAR MORE POWER of people than first even

I had to do a little research to realise what bahman is meaning, which is specifically in relation to the mathematics of functions (imagine a graph which plots an x and y axis, such that there is some relation between the x and y coordinates, this relationship is the function). Any function (curve on an x y axis) which varies continuously, can in theory be divided (artificially) at an infinite number of points along its curve. This is called a magnitude. Examples of magnitude are, time, distance, etc. you can divide them (artificially) infinitely. That is the nature of a continuous function. Now, the reason you would want to “limit” a function, is so you can find its derivative (the “slope” at any particular point on the curve). An example of a derivative of a continuous function is, as bahman is using, velocity, which is v = d/t, where v = velocity, d = distance travelled, and time = time the thing travelled in that distance. V is found whereby distance and time are plotted on this graph such that they covary, at any artificial point on the curve, they will have different but related values. The relation between those two variables is the velocity, which is the slope (angle) of the curve plotted by those two variables at any particular point on the curve.

But, there is a problem with trying to find this slope for a point. To find the slope, you have to use an artificial limit on a section of the curve you want to find the slope value of. So, you create a set of limits, or divisions on that curve, such that you can work out the relationship between those two values based on their difference between those two points on the curve.

When you do this, you are dividing something continuous, creating an artificial division on something which is, in reality, whole and can be divided infinitely.

As mentioned earlier, something discrete is like a point which has the SAME value throughout the whole of its division. Now, the artificially divided continuous function does NOT possess such a quality, and as such, cannot be viewed as discrete. Because you can infinitely divide a continuous function, the division is always containing some CHANGE in its slope throughout the section. This is opposite to a discrete point like coordinate, which is just that a point.

I hope you understand now WHAT bahman is attempting to prove, and why he cannot prove it.

I am not that clear still about The mathematics behind it, as I just educated myself on it over the past few days, and so bahman will occasionally go off on some mathematical prosings or transformations which are currently beyond my understanding, but, it still doesn’t change the fact that what he is attempting is not logically possible.

Let me explain the problem to you with a simple function: f(x)=x^2. We want to calculate the derivative of this function. To do so we need to calculate Df=f(x+dx)-f(x) (dx be a small number) which is (x+dx)^2=x^2+2*dx*x+dx^2-x2=2*dx*x+dx^2=dx*(2*x+dx). The derivative then can be calculated as df/dx=dx*(2*x+dx)/dx. We can safely remove dx from the numerator and denominator provided that dx is not zero. We then get df/dx=(2*x+dx). The problem is that dx is a nonzero number so we cannot neglect dx on the right side so we have a residue that is very small but we cannot ignore it. If we set dx=0 then we have to deal with 0/0 which is undefined but that is the only regime that the residue is zero.

Dimebag wrote: ↑Sun Feb 28, 2021 12:33 pm Bahman, I came across a source which discusses much of what you seem to be attempting, seemingly with little to no clear resolve, you may find it here:

https://plato.stanford.edu/entries/continuity/#1

Much if not most of it went over my head, but you may find it useful. But, I think you will find you are not alone in your attempts.

Oh, thanks. I will read it shortly.

Dimebag wrote: ↑Sun Feb 28, 2021 12:51 am

Age wrote: ↑Sat Feb 27, 2021 11:12 pm You used the operative word here, 'parts'.

Any time any one is looking at any 'thing' in regards to 'its' 'parts', then they will, and will 'have to', see 'discrete'. By using the word 'parts', then one can ONLY see in relation to separated 'things'.

Because absolutely EVERY thing is relative to the observer, if one is LOOKING FOR or LOOKING AT 'parts', then 'parts', or 'separation', is what they can and will ONLY SEE.

See, what actually happened, in the days of when this was being written, is those human beings did not fully recognize nor accept just how much influence and power words, themselves, have over them.

Just look at the words used here;

" If one 'divides' a 'continuous function' into 'small enough parts' you might consider them to be 'discrete jumps' ".

Now, if we want to break this down, ourselves, into smaller parts, then what can be seen is that 'if one does 'divide' ANY 'thing' into 'smaller parts', then it is NOT just a fact that they 'might' consider the 'smaller parts' to be 'discrete jumps' but an absolute FACT that they would 'HAVE TO' consider the actual 'individual and separated smaller parts' to be 'discrete jumps'. One has NO choice in or over this matter.

If one looks at 'parts', then one 'has to' see, and thus can only see, 'separated parts', 'distinction', and thus 'discrete jumps'.

This, by the way, does NOT mean that 'discrete' NOR 'discrete jumps' actually exist. This is just what this one person is seeing, and saying, there is.

'See', if one 'says' there are 'parts', then that one will 'see', separated and distinct, 'parts'. Just like when one 'says' there is 'one thing', then that one will 'see', just, 'one thing'. However, if one 'says' there is 'one thing' that can be broken down into 'parts', then what that one will 'see' is 'one thing' with separated and distinct 'parts'.

What 'you' 'say' to 'yourself' has far more influence OVER 'you', than is FULLY REALIZED when this is first read or heard. But as human beings keep evolving along this starts off gradually being realized and accepted becoming more and more exponentially realized and accepted.

The thoughts, or thinking, within a head actually has FAR MORE POWER of people than first even

I had to do a little research to realise what bahman is meaning, which is specifically in relation to the mathematics of functions (imagine a graph which plots an x and y axis, such that there is some relation between the x and y coordinates, this relationship is the function). Any function (curve on an x y axis) which varies continuously, can in theory be divided (artificially) at an infinite number of points along its curve. This is called a magnitude. Examples of magnitude are, time, distance, etc. you can divide them (artificially) infinitely. That is the nature of a continuous function. Now, the reason you would want to “limit” a function, is so you can find its derivative (the “slope” at any particular point on the curve). An example of a derivative of a continuous function is, as bahman is using, velocity, which is v = d/t, where v = velocity, d = distance travelled, and time = time the thing travelled in that distance. V is found whereby distance and time are plotted on this graph such that they covary, at any artificial point on the curve, they will have different but related values. The relation between those two variables is the velocity, which is the slope (angle) of the curve plotted by those two variables at any particular point on the curve.

But, there is a problem with trying to find this slope for a point. To find the slope, you have to use an artificial limit on a section of the curve you want to find the slope value of. So, you create a set of limits, or divisions on that curve, such that you can work out the relationship between those two values based on their difference between those two points on the curve.

When you do this, you are dividing something continuous, creating an artificial division on something which is, in reality, whole and can be divided infinitely.

As mentioned earlier, something discrete is like a point which has the SAME value throughout the whole of its division. Now, the artificially divided continuous function does NOT possess such a quality, and as such, cannot be viewed as discrete. Because you can infinitely divide a continuous function, the division is always containing some CHANGE in its slope throughout the section. This is opposite to a discrete point like coordinate, which is just that a point.

I hope you understand now WHAT bahman is attempting to prove, and why he cannot prove it.

I still do not, but thank you very much for taking the time to try to explain this to me.

I wonder, however, why ANY one would even attempt to prove something, which that can NOT prove? Unless of course they have preexisting BELIEFS, which they are just trying to find ANY thing, in the hope that they will back up and support those BELIEFS.

Also, if some 'thing' can NOT be proved, then this might be a CLEAR SIGN that one 'needs' to CHANGE their BELIEFS and/or the way they LOOK at 'things'