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What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill
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On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


Start here

https://en.wikipedia.org/wiki/Electr..._wave_equation

then look up permittivity and permeability of free space
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On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


You have to bear in mind that the metre is an arbitrary distance based
on the circumference of the Earth, and a second was a fraction of the
duration of the Earth's orbit, finally fixed as a number that is
9,192,631,770 cycles of the radiation produced by the transition between
two levels of the caesium 133 atom.

Admittedly we have got nothing better to describe the speed of light,
but it does explain why that speed when calculated isn't a conveniently
memorable number.

Jim

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On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?


To save you wading through a load of vector partial differential
equations have a look at the equation under the text "which identify"
in the section:
https://en.wikipedia.org/wiki/Maxwell's_equations#Vacuum_equations,_electromagne tic_waves_and_speed_of_light

The summary is:
Speed of light (or other EM radiation) is one over the square root
of (μ (permeability) times ε (permittivity)).

Permeability and permittivity are measures of the magnetic and
electric properties (respectively) of a material.

A common practice is to take the permeability and permittivity of a
material and divide them by the permeability and permittivity of a
vacuum. The resulting ratios are known as the relative permeability
and relative permittivity respectively.

For people familiar with electronic components relative permittivity
is also known as dielectric constant in capacitors. It's the factor
by which the capacitance is multiplied due to using a given dielectric
material as an insulator rather than vacuum (or, more practically, air).

Some more reading:
https://en.wikipedia.org/wiki/Permeability
https://en.wikipedia.org/wiki/Permittivity

The number you get will depend on the units you use. If you use something
other than SI units (metres, kilograms, seconds, etc) you'll get a
different number, e.g. 186,282 miles per second. (But it should be the
same speed, just expressed in different units.)


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On 24/12/2017 20:43, Bill Wright wrote:

What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?


The electro-magnetic behaviour of space is described by Maxwell's
Equations. As newshound has suggested, it is possible to show* that a
wave equation is a possible solution of Maxwell's Equations, and that
the speed of the resulting wave would be equal to ...
1 / sqroot( permittivity of space * permeability of space)
.... and that this value is exactly equal to the measured speed of light
in space. This is how we know that light is an electro-magnetic wave.

* This is science speak:

It is trivial to show that = an undergrad can prove it
It is easy to show that = a postgrad can prove it
It may be proved that = The prof can prove it

In this particular case, I was able to prove it at uni, and did so
during a physics tutorial, which, I discovered much later from a
bus-stop conversation between another student who'd been present with my
then girl-friend, gave me something of a reputation for the subject.
But I wouldn't want to be asked to prove it now!


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On 24/12/2017 22:01, Indy Jess John wrote:
On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


You have to bear in mind that the metre is an arbitrary distance based
on the circumference of the Earth, and a second was a fraction of the
duration of the Earth's orbit, finally fixed as a number that is
9,192,631,770 cycles of the radiation produced by the transition between
two levels of the caesium 133 atom.

Admittedly we have got nothing better to describe the speed of light,
but it does explain why that speed when calculated isn't a conveniently
memorable number.


I think what he's asking is why it's a constant, ie what makes it so,
and why it is what it is rather than something else?

Got any answer?
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replying to Bill Wright, Iggy wrote:
Lies, Liars and Frauds...to put it precisely. Space "science" (laughable
non-science) is the biggest bunch of contradictions ever. They claim
authority, simply make an outlandish statement, never provide any proof nor
duplication and the droolers obey. They tell us only what Real Science has
duplicated and measured, though their patently ridiculous Big Bang crushed it
all. Therefore, your speeds can't exist...according to them. However, your
speeds must and do exist...according to them.

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On 24/12/17 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


Not everything has a cause. Some things Just Are.

God was the traditional explanation of course.


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private property.

Karl Marx

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On 24/12/17 20:59, newshound wrote:
On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


Start here

https://en.wikipedia.org/wiki/Electr..._wave_equation

then look up permittivity and permeability of free space


But that doesnt do more than transform the question into 'why is that
the value of the permittivity and permeability of free space'?



--
The theory of Communism may be summed up in one sentence: Abolish all
private property.

Karl Marx

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On 24/12/17 22:53, Norman Wells wrote:
On 24/12/2017 22:01, Indy Jess John wrote:
On 24/12/2017 20:43, Bill Wright wrote:
What are the parameters that set the speed of electromagnetic
transmission in a vacuum? I've googled everywhere but I can't find the
answer. It's easy enough to find the figure but WHY? Why not
29,979,245.8 metres per second or 2,997,924,580 metres per second?

Bill


You have to bear in mind that the metre is an arbitrary distance based
on the circumference of the Earth, and a second was a fraction of the
duration of the Earth's orbit, finally fixed as a number that is
9,192,631,770 cycles of the radiation produced by the transition
between two levels of the caesium 133 atom.

Admittedly we have got nothing better to describe the speed of light,
but it does explain why that speed when calculated isn't a
conveniently memorable number.


I think what he's asking is why it's a constant, ie what makes it so,
and why it is what it is rather than something else?

Got any answer?


Because if it wasnt what it is, the world wouldn't be what it is, and in
all likelihood he wouldn't be wherever here is to ask such damn fool
questions.


--
New Socialism consists essentially in being seen to have your heart in
the right place whilst your head is in the clouds and your hand is in
someone else's pocket.



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On 25/12/2017 08:21, The Natural Philosopher wrote:
On 24/12/17 22:53, Norman Wells wrote:
On 24/12/2017 22:01, Indy Jess John wrote:


Admittedly we have got nothing better to describe the speed of light,
but it does explain why that speed when calculated isn't a
conveniently memorable number.


I think what he's asking is why it's a constant, ie what makes it so,
and why it is what it is rather than something else?

Got any answer?


Because if it wasnt what it is, the world wouldn't be what it is, and in
all likelihood he wouldn't be wherever here is to ask such damn fool
questions.


But it's a philosophical question. And I thought from your name that
you might have an answer.

Anyway, aren't all philosophical questions damn fool questions?



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On 25/12/2017 09:25, Tim Streater wrote:

... life would not be possible in
most of the resulting universes.


"Life as we know it" - to more or less quote Dr Spock.
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In message , Tim Streater
writes
AIUI, there are about 26 physical constants (such as speed of light)
for the values of which there is no theoretical explanation known
today. That is, it's as if God (I use the term for convenience) has 26
knobs to turn to set these values and launch the universe. They could
have any values, these constants, and life would not be possible in
most of the resulting universes.


Which raises the interesting question of whether alternative universes
exist in which some or all of those constants have different values.
--
John Hall "George the Third
Ought never to have occurred.
One can only wonder
At so grotesque a blunder." E.C.Bentley (1875-1956)
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On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.


Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.

Here's something that may help:

http://www.physics.sfsu.edu/~lwilliam/sota/anth/
anthropic_principle_index.html



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On Mon, 25 Dec 2017 08:18:36 +0000, The Natural Philosopher wrote:


"The theory of Communism may be summed up in one sentence: Abolish all
private property."

Marx was such a stupid ****. No one capable of critical thinking can
possibly take his daft ideas seriously. I wish I could have sneaked up
behind him in the British Library reading room and planted a stiletto in
the back of his thick skull.



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On 25/12/17 09:10, Norman Wells wrote:
On 25/12/2017 08:21, The Natural Philosopher wrote:
On 24/12/17 22:53, Norman Wells wrote:
On 24/12/2017 22:01, Indy Jess John wrote:


Admittedly we have got nothing better to describe the speed of
light, but it does explain why that speed when calculated isn't a
conveniently memorable number.

I think what he's asking is why it's a constant, ie what makes it so,
and why it is what it is rather than something else?

Got any answer?


Because if it wasnt what it is, the world wouldn't be what it is, and
in all likelihood he wouldn't be wherever here is to ask such damn
fool questions.


But it's a philosophical question.Â* And I thought from your name that
you might have an answer.


I do, and that is it.


Anyway, aren't all philosophical questions damn fool questions?


No, often they are the most fundamental questions of all.

You are asking the basic question - why is the world the way it is?

And seeking an answer based on a notion of causality - that is, because
something *caused* it to be that way.

Causality, however is a human notion and not necessarily ubiquitous.

If you insist that it is, you will arrive at notions of a Creator, be it
a Big Bang, or a weird supernatural Intelligence. Merely in order to
complete a chain of causality.

The answer is to not ask a question framed in terms of normal relative
reality about the nature of absolute reality.

It's as silly as asking what color B flat is.

The neatest 'explanation' is Taoism. The Tao is that which exists
through itself. I.e. it perpetuates itself. The nature of the Tao is
whatever yiu consider the world to be made from.

In this case electromagnetic entities in a space time causality matrix.

well its different from God and his Angels, but not much.







--
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This makes me unfit for the company of people of a Left persuasion, and
all women"
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On 25/12/17 09:51, John Hall wrote:
In message , Tim Streater
writes
AIUI, there are about 26 physical constants (such as speed of light)
for the values of which there is no theoretical explanation known
today. That is, it's as if God (I use the term for convenience) has 26
knobs to turn to set these values and launch the universe. They could
have any values, these constants, and life would not be possible in
most of the resulting universes.


Which raises the interesting question of whether alternative universes
exist in which some or all of those constants have different values.


Since by definition we can't exist in them, how could we tell?


--
In todays liberal progressive conflict-free education system, everyone
gets full Marx.
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On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.


Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.


And you think that science has nowt to do with philosophy? How quaint!"

Here's something that may help:

http://www.physics.sfsu.edu/~lwilliam/sota/anth/
anthropic_principle_index.html


Pure philosophy really.





--
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On 25/12/17 11:50, Cursitor Doom wrote:
On Mon, 25 Dec 2017 08:18:36 +0000, The Natural Philosopher wrote:


"The theory of Communism may be summed up in one sentence: Abolish all
private property."

Marx was such a stupid ****. No one capable of critical thinking can
possibly take his daft ideas seriously. I wish I could have sneaked up
behind him in the British Library reading room and planted a stiletto in
the back of his thick skull.


I'll drink to that mate.

Unfortuntaely Marxism is an inevitabe result of taking peasants off
fields where nature insists on smome basic common sense, and plonking
them in factories and cities, where nature doesn't feature and their
innate capacity for pompous silliness can flourish unbounded, until you
get the likes of Caroline Lucas or Jeremey Corbyn.




--
Its easier to fool people than to convince them that they have been fooled.
Mark Twain




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On 25/12/2017 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.


Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.


Just how old are you then?
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On 25/12/2017 11:51, The Natural Philosopher wrote:
On 25/12/17 09:10, Norman Wells wrote:
On 25/12/2017 08:21, The Natural Philosopher wrote:
On 24/12/17 22:53, Norman Wells wrote:
On 24/12/2017 22:01, Indy Jess John wrote:


Admittedly we have got nothing better to describe the speed of
light, but it does explain why that speed when calculated isn't a
conveniently memorable number.

I think what he's asking is why it's a constant, ie what makes it
so, and why it is what it is rather than something else?

Got any answer?

Because if it wasnt what it is, the world wouldn't be what it is, and
in all likelihood he wouldn't be wherever here is to ask such damn
fool questions.


But it's a philosophical question.Â* And I thought from your name that
you might have an answer.


I do, and that is it.

Anyway, aren't all philosophical questions damn fool questions?


No, often they are the most fundamental questions of all.


Even so, it doesn't stop them being damn fool questions.

You see, questions require answers that actually answer the questions.
If you have to employ a philosopher, especially on Christmas Day when
they charge triple time, to spend hours beating about the bush, that's
proof enough to me that they're damn fool questions that were pointless
to ask in the first place.

You are asking the basic question - why is the world the way it is?


I am? Oh, OK, you're the philosopher.

And seeking an answer based on a notion of causality - that is, because
something *caused* it to be that way.

Causality, however is a human notion and not necessarily ubiquitous.

If you insist that it is, you will arrive at notions of a Creator, be it
a Big Bang, or a weird supernatural Intelligence. Merely in order to
complete a chain of causality.


What you really mean then is 'God knows!'.

The answer is to not ask a question framed in terms of normal relative
reality about the nature of absolute reality.

It's as silly as asking what color B flat is.


Well, it's green. Any fool knows that.

At least the middle one is. I don't know about octaves up or down. I
never go there.

The neatest 'explanation' is Taoism. The Tao is that which exists
through itself. I.e. it perpetuates itself. The nature of the Tao is
whatever yiu consider the world to be made from.

In this case electromagnetic entities in a space time causality matrix.

well its different from God and his Angels, but not much.


I'm beginning to wish I hadn't asked. But thanks, and a happy Christmas
anyway.
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On Mon, 25 Dec 2017 11:57:21 +0000, The Natural Philosopher wrote:

On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.


Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.


And you think that science has nowt to do with philosophy? How quaint!"



Natural philosophy was the term for science back in Newton's day. I'm
guessing you must surely know that, since it's your adopted moniker.




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On Mon, 25 Dec 2017 12:36:49 +0000, Norman Wells wrote:

Just how old are you then?


I think you need to address that to NP.



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On Mon, 25 Dec 2017 12:49:16 +0000, Norman Wells wrote:


You see, questions require answers that actually answer the questions.
If you have to employ a philosopher, especially on Christmas Day when
they charge triple time, to spend hours beating about the bush, that's
proof enough to me that they're damn fool questions that were pointless
to ask in the first place.


Who's your favourite philosopher? Mine's Arthur S. Brilliant bloke!



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On 25/12/2017 13:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 12:36:49 +0000, Norman Wells wrote:

Just how old are you then?


I think you need to address that to NP.


Yes. Can you pass it on?

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On 25/12/2017 11:51, The Natural Philosopher wrote:
It's as silly as asking what color B flat is.


The BBC managed to convert 'gravitational ripples' (or whatever)
into 'sound' !.

Some blind people use 'seeing' canes that give them some sort
of audible impression what they are about to fall over.
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On 25/12/2017 12:00, The Natural Philosopher wrote:
On 25/12/17 11:50, Cursitor Doom wrote:
On Mon, 25 Dec 2017 08:18:36 +0000, The Natural Philosopher wrote:


"The theory of Communism may be summed up in one sentence: Abolish all
private property."

Marx was such a stupid ****. No one capable of critical thinking can
possibly take his daft ideas seriously. I wish I could have sneaked up
behind him in the British Library reading room and planted a stiletto in
the back of his thick skull.


I'll drink to that mate.

Unfortuntaely Marxism is an inevitabe result of taking peasants off
fields where nature insists on smome basic common sense, and plonking
them in factories and cities, where nature doesn't feature and their
innate capacity for pompous silliness can flourish unbounded, until you
get the likes of Caroline Lucas or Jeremey Corbyn.





"It is enough that the people know there was an election. The people who
cast the votes decide nothing. The people who count the votes decide
everything." Stalin.
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On 25/12/17 13:43, Cursitor Doom wrote:
On Mon, 25 Dec 2017 11:57:21 +0000, The Natural Philosopher wrote:

On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.

Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.


And you think that science has nowt to do with philosophy? How quaint!"



Natural philosophy was the term for science back in Newton's day. I'm
guessing you must surely know that, since it's your adopted moniker.


Nope, science is the modern name for natural philosophy.

It ries to pretend it isnt a branch of philsophy. This leads to huge
mistakes - like 'climate change'




--
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Josef Stalin

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On 25/12/17 13:54, Tim Streater wrote:
Which raises the interesting question of whether alternative universes
exist in which some or all of those constants have different values.


Indeed it does and now you're in the realm of metaphysics.

There are however some speculative hypotheses which imply they do.


Again yuputr are staring out with baseless assumptions.

The notion of a universe, and indeed an alternative one, is itself
anthropic.

What is, just is.

....We assume, irrespective of whether we have notions about it, or not...


--
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On 25/12/2017 18:09, The Natural Philosopher wrote:
On 25/12/17 13:54, Tim Streater wrote:
Which raises the interesting question of whether alternative
universes exist in which some or all of those constants have
different values.


Indeed it does and now you're in the realm of metaphysics.

There are however some speculative hypotheses which imply they do.


Again yuputr are staring out with baseless assumptions.

The notion of a universe, and indeed an alternative one, is itself
anthropic.

What is, just is.

...We assume, irrespective of whether we have notions about it, or not...



I just don't see where any of this speculation gets you? It's possible
to hypothesise anything at all, but if it can't be measured or observed
you can't take it any further. Discussion about alternative universes is
rightly treated as (science) fiction and fantasy, rather than philosophy.
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On Mon, 25 Dec 2017 12:49:16 +0000, Norman Wells wrote:

I'm beginning to wish I hadn't asked.


So why did you? There must be more appropriate groups.
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On 25/12/2017 18:09, The Natural Philosopher wrote:
On 25/12/17 13:54, Tim Streater wrote:
Which raises the interesting question of whether alternative
universes exist in which some or all of those constants have
different values.


Indeed it does and now you're in the realm of metaphysics.

There are however some speculative hypotheses which imply they do.


Again yuputr are staring out with baseless assumptions.

The notion of a universe, and indeed an alternative one, is itself
anthropic.

What is, just is.


If only philosophers through the ages had appreciated that universal
wisdom, they'd have saved so much time, and perhaps been able to do
something useful instead.

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In article ,
Norman Wells wrote:

It's as silly as asking what color B flat is.


Well, it's green. Any fool knows that.


And synaesthetes ...
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On 25/12/2017 11:51, The Natural Philosopher wrote:

It's as silly as asking what color B flat is.


I was assured it is octoroon.
In the absence of a better answer, I will stick with that.

Jim


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On Mon, 25 Dec 2017 18:46:32 +0000, Tim Streater wrote:

unable to detect. This is called dark matter.

Mind you, that idea could be scrapped at any time.


They're on about "dark energy" now, to account for the *acceleration* in
the expansion of the universe!
Must be a nightmare being in theoretical physics nowadays.



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On Mon, 25 Dec 2017 18:07:11 +0000, The Natural Philosopher wrote:

On 25/12/17 13:43, Cursitor Doom wrote:
On Mon, 25 Dec 2017 11:57:21 +0000, The Natural Philosopher wrote:

On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name
that you might have an answer.

Natural Philosophy has nowt much to do with philosophy; it's simply
the archaic term for science.

And you think that science has nowt to do with philosophy? How
quaint!"



Natural philosophy was the term for science back in Newton's day. I'm
guessing you must surely know that, since it's your adopted moniker.


Nope, science is the modern name for natural philosophy.

It ries to pretend it isnt a branch of philsophy. This leads to huge
mistakes - like 'climate change'



I think you've had quite enough to drink now, NP. You're just re-
arranging what I said earlier.



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On 25/12/17 20:43, Cursitor Doom wrote:
On Mon, 25 Dec 2017 18:07:11 +0000, The Natural Philosopher wrote:

On 25/12/17 13:43, Cursitor Doom wrote:
On Mon, 25 Dec 2017 11:57:21 +0000, The Natural Philosopher wrote:

On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name
that you might have an answer.

Natural Philosophy has nowt much to do with philosophy; it's simply
the archaic term for science.

And you think that science has nowt to do with philosophy? How
quaint!"


Natural philosophy was the term for science back in Newton's day. I'm
guessing you must surely know that, since it's your adopted moniker.


Nope, science is the modern name for natural philosophy.

It ries to pretend it isnt a branch of philsophy. This leads to huge
mistakes - like 'climate change'



I think you've had quite enough to drink now, NP. You're just re-
arranging what I said earlier.



You think that because you can't do critical thinking. Probably down to
a State Education.

Science was not 'called natural philosophy'

Science did not exist. Natural philosophy did, and still does.








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On Monday, 25 December 2017 18:07:14 UTC, The Natural Philosopher wrote:
On 25/12/17 13:43, Cursitor Doom wrote:
On Mon, 25 Dec 2017 11:57:21 +0000, The Natural Philosopher wrote:
On 25/12/17 11:44, Cursitor Doom wrote:
On Mon, 25 Dec 2017 09:10:43 +0000, Norman Wells wrote:

But it's a philosophical question. And I thought from your name that
you might have an answer.

Natural Philosophy has nowt much to do with philosophy; it's simply the
archaic term for science.

And you think that science has nowt to do with philosophy? How quaint!"



Natural philosophy was the term for science back in Newton's day. I'm
guessing you must surely know that, since it's your adopted moniker.


Nope, science is the modern name for natural philosophy.

It ries to pretend it isnt a branch of philsophy. This leads to huge
mistakes - like 'climate change'


That's a major problem with 'science' today. The experiments are done, the results analysed and p value calculated, but somewhere along the line the illogic of the experimenter completely screwed up, making the conclusions largely worthless.


NT
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On Monday, 25 December 2017 18:09:14 UTC, The Natural Philosopher wrote:
On 25/12/17 13:54, Tim Streater wrote:


Which raises the interesting question of whether alternative universes
exist in which some or all of those constants have different values.


Indeed it does and now you're in the realm of metaphysics.

There are however some speculative hypotheses which imply they do.


Again yuputr are staring out with baseless assumptions.

The notion of a universe, and indeed an alternative one, is itself
anthropic.

What is, just is.

...We assume, irrespective of whether we have notions about it, or not...



'Alternate universe' strikes me as a self contradiction. Thus they don't exist.


NT
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