Einstein on the train

How does science work? And what's all this about quantum mechanics?

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Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

I just finally read through the posts above and thought to point out some things in response to Age and uwot's discussion as well as add my two cents thus far. Note I still have not read the rest of the pdf Willy. But I already know it will be good. I liked your point about wanting to have read something like this when 15. I share this view and believe you have done better than most on covering a lot in so little space.

Age was asking something about the 9.8 m/s^2 acceleration due to gravity 'fact'. I may be able to bridge the apparent conflict he/she has to uwot's expanations given somethings I had problems with before trying to make sense of the distinction of what many think is or is not 'empirical'.

Galileo's original 'proofs' were discussed in philosophical dialect similar to Plato's dialogues using Socrates as his voice. The original arguments made by Galileo were NOT empirical but strictly logical with a trivial non-measurement 'fact'. The follow-up experiments that Galileo used was intended to demonstrate his prior logic by USING measurement to express it. The incidental nature to find the measure of acceleration due to gravity is the 'fact' part that is trivially distinct from the logic. That 'fact' (the measure) is changeable and also only applies to a specific 'instantaneous' point in height from the center of the Earth as well as to other large objects, such as mountains that may distort literal local measurements.

The actual logic Galileo argued was dismissed for odd reasons by some people who took insult by his indirect reference to them with such names as "Simplicio" as a reference of insult of those who can't think logical. The brick with the imaginary link suffices to argue THAT objects accelerate. The actual experiments only provide direct experiment to those unable or unwilling to accept. The logic of the independence of the force of gravity was due to the following kind of thinking:

Imagine you are pulling your one or more of your children on a sled. The energy and/or force needed to pull two children of the same mass requires twice the force and expended energy. What Galileo was saying about gravity in contrast to Aristotle was that the Earth pulls on ANY mass with the same rate as though pulling two children is equivalent to pulling one ....or even a thousand, etc. Obviously if you were told this, it would make you ask how the Earth could 'know' what the mass is to adjust the manpower at will, greater for larger objects versus smaller ones.

Galileo used thought experiments with the trivial common knowledge that anybody without extensive experience could follow. If you hold up a brick and drop it from a specific height, we assume this to be the same if we repeat it precisely or even move slightly to the left or right to repeat this. Now imagine doing this simultaneously by holding two bricks at the same height. You can logically realize that intuitively that dropping the two bricks side by side would hit the ground at the same time. Now just imagine the two bricks, two distinct masses, be conjoined by an imaginary chain. Dropping one or two independently makes no difference. Thus dropping one mass versus twice the mass at the same height will hit the ground together.

There is more to these thought experiments that suffice to 'prove' using logic and a minimal of non-numerical measurements in order to determine that objects of different masses fall independent of their mass. What DOES differ would be what occurs when they hit the ground. The heavier objects would then have an additive effect and can determine more or less damage to something it falls on.

The point is this kind of 'fact' is the logical one and has closure. The experiment to demonstrate this with different inclines and measurements were to show that whatever the measure of the ratio of distance per unit time is for any mass, when you fix the distance, all masses falling from the same height will complete the fall (or drop from an incline) at the exact same time. He used the incline with the reasoning that although that would slow down the fall, the same would occur in sync with any objects from the same set up.

So the actual literal measure of acceleration due to gravity is irrelevant. THAT 'fact' is what Age was confusing to the 'fact' that objects fall at the same rate. He also used Zeno's paradox of non-movement to show that objects should accelerate because if you begun with any relative time 0, that 'velocity' is 0. Any final velocity greater requires a CHANGE of variable continuous degrees of speed beginning at zero to that final rate. Otherwise the speed would instantly jump from zero to the final velocity.

So uwot, for future reference, maybe this might help to be clarified in distinction for others like, Age here, to differentiate between precise actual constants versus the proportional relationships. (most are not as familiar with the math part representing proportionality and the distinction of the relevant constants used, which may be arbitrary and changing.

[con't next thread]
Logik
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Re: Einstein on the train

Post by Logik »

Scott Mayers wrote: Wed Mar 20, 2019 3:43 pm So uwot, for future reference, maybe this might help to be clarified in distinction for others like, Age here, to differentiate between precise actual constants versus the proportional relationships. (most are not as familiar with the math part representing proportionality and the distinction of the relevant constants used, which may be arbitrary and changing.
The issue is not ONLY about precision. Yes - we could argue till the cows come home whether g = 9.8 m/s^2

g = 9.81 m/s^2
g = 9.807 m/s^2
g = 9.8077 m/s^2
g= 9.80665 m/s^2

Ceteris paribus nitpickers will still insist on infinite precision otherwise 0.999... = 1. And then they will dance on your metaphorical tombstone because they managed to "contradict you".

The greater problem is context! Context, context, context.

These numbers don't exist in a vacuum. The value of g is 9.81 at sea level at the equator. Are you at sea level? Are you at the equator?

g is a function of the distance to the centre of Earth which is ABOUT 6400km, but not exactly because Earth is NOT a sphere and its surface is not uniform.

And so it's really deceptive to talk about g as a constant! When you say "g = 9.81 m/s^2" you are quite literally excluding about 95% of the habitable surface of the Earth.

Depending on your position on Earth g is anywhere between 9.7639 m/s2, and 9.8337 m/s2
Last edited by Logik on Wed Mar 20, 2019 4:14 pm, edited 3 times in total.
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

For uwot and Age con't,

The other problem I know Age was not understanding that you, uwot, at least linked for his/her own follow-up was to another concern I too had when I first wanted to follow but is too often skipped over:

You, uwot, did an excellent job connecting some features of doppler but the question to which Age was thinking is HOW can they determine THAT the Doppler effect determines distance? The missing details are, the initial close star distance as determined by parallax, the math of the inverse square law of luminescence of stars, and how they determined the standard distances based upon brightness BEFORE you could use Doppler to compare with. That might be something you could add to help clarify. (next edition?)

Anyways, I think this is enough to help clarify for Age to uwot the misinterpretations and what might be of value to improve upon the confusion of those similar questions any 15 year old might be wandering too.

I like your effort uwot and think it is necessarily lacking. I like the connectivity of it and have to ask which 'heroes' of science popularizers were your favorite?

Mine at present are the two Brians: Brian Cox and Brian Greene, and much earlier, Carl Sagon. Brian Greene added describing alternate theories without bias to his own support for the standard factors. Jim Al Khalili, I held some contention with on his physics but has the best series on chemistry. And remember the series "Connections" by James Burke? I sense you share some of these as well. I appreciate HOW you wrote, with both humor, respect (non-insult to those being skeptical), and to how you fluidly connected the various parts of the different and sometimes conflicting views in your own creative way that at least would make novel thinkers feel better confidence at relating to science with less confusion.
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

Logik wrote: Wed Mar 20, 2019 4:03 pm
Scott Mayers wrote: Wed Mar 20, 2019 3:43 pm So uwot, for future reference, maybe this might help to be clarified in distinction for others like, Age here, to differentiate between precise actual constants versus the proportional relationships. (most are not as familiar with the math part representing proportionality and the distinction of the relevant constants used, which may be arbitrary and changing.
The issue is not ONLY about precision. Yes - we could argue till the cows come home whether g = 9.8 m/s^2

g = 9.81 m/s^2
g = 9.807 m/s^2
g = 9.8077 m/s^2
g= 9.80665 m/s^2

Ceteris paribus nitpickers will still insist on infinite precision otherwise 0.999... = 1. And then they will dance on your metaphorical tombstone because they managed to "contradict you".

The greater problem is context! Context, context, context.

These numbers don't exist in a vacuum. The value of g is 9.81 at sea level at the equator. Are you at sea level? Are you at the equator?

g is a function of the distance to the centre of Earth which is ABOUT 6400km, but not exactly because Earth is NOT a sphere and its surface is not uniform.

And so it's really deceptive to talk about g as a constant! When you say "g = 9.81 m/s^2" you are already implying that you are NOT talking about Everest or Kuala Lumpur.

Depending on your position on Earth g is anywhere between 9.7639 m/s2, and 9.8337 m/s2
The actual way of expressing this is that 'g' is defined as the constant of gravitational field constant. Its' a varying constant but more generally expressed universally as:

F = (Gm1m2)/d²


But I'm guessing you're razzing me. The 'context' above is understood to be changing. You're making it only more confusing than it has to be with respect to what Age was saying. The constant is itself a constant of proportionality relative to the more general Universal Constant of Gravitation, G, in the formula above. Earth's gravitational field constant is specifically tied to that formula above by placing one mass with the Earth's mass and the particular distance from the center of the Earth to a specific height, 'd' in the forumula above. "G" then is the FIXED constant.

F = ma = m1g = (Gm1m2)/d²

then g = (Gm2)/d²

where g is the needed constant of gravity at distance from the center of the Earth, d, and where m2 is the Earth's mass.

Substitute 5.972 × 10²⁴kg for the Earth's mass, m2, and 6.67408 × 10⁻¹¹ m³/ kg s² for G

Then solve for g for the precise measure using a d to whatever elevation from the center you want from where you are. Sea level differs at the equator but the average circumference of the earth is 40,075 km at the equator.

Now, while this precision is more correct, it is intimidating and unimportant to deal with the constants when one is learning the logic-side of the issue. So you aren't helping. That is the insignificant 'facts' that were muddling the issue Age was trying to express, as I understood.

Edit: added the average circumference to the earth at the equator if you want to try to determine what that 9.8 m/s² average came from using the math I provided. I'm not going to try to do it here in HTML. It was already difficult enough doing this above. Now imagine if Willy were to have had to use html to express this to a 15 year old wanting to learn the logic of science! Would you want to sign up for that physics class after trying to go through all of that?
Edit: now added superscripts to make it easier to read.
Last edited by Scott Mayers on Wed Mar 20, 2019 6:06 pm, edited 1 time in total.
Logik
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Re: Einstein on the train

Post by Logik »

Scott Mayers wrote: Wed Mar 20, 2019 4:57 pm F = (Gm1m2)/d^2


(...)
Now, while this precision is more correct, it is intimidating and unimportant to deal with the constants when one is learning the logic-side of the issue. So you aren't helping. That is the insignificant 'facts' that were muddling the issue Age was trying to express, as I understood.
Only two things I want to point out.

1. Observe how you chose Newton's equation, not Einstein's one. And so my point (as before) stands. Context!

You have constrained yourself to contexts in which Newton's equation works and thus you implicitly exclude all contexts in which they don't.
Einstein's equations are generalisations of Newton's equation. They reduce down to Newton's equations with a margin of error so trivial that nobody cares.

Still: you ignore my point. Every scientific theory so far comes with a fine-print that we call 'domain of applicability' a.k.a context of validity.

2. Age's intellectual journey is still at its infancy. He is focused entirely on consistency. He pursues consistency religiously and idiomatically. He nitpicks at any and all inconsistencies - both small and big, to the point that if he were aware that Newton's equations were 'imprecise' he would insist that you used Einstein's equations - even here. On Earth even though the margin of error is insignificant.

He still has an all-or-nothing mindset. If it's not perfect it's junk.
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

Logik wrote: Wed Mar 20, 2019 6:03 pm
Scott Mayers wrote: Wed Mar 20, 2019 4:57 pm F = (Gm1m2)/d^2


(...)
Now, while this precision is more correct, it is intimidating and unimportant to deal with the constants when one is learning the logic-side of the issue. So you aren't helping. That is the insignificant 'facts' that were muddling the issue Age was trying to express, as I understood.
Only two things I want to point out.

1. Observe how you chose Newton's equation, not Einstein's one. And so my point (as before) stands. Context!

You have constrained yourself to contexts in which Newton's equation works and thus you implicitly exclude all contexts in which they don't.
Einstein's equations are generalisations of Newton's equation. They reduce down to Newton's equations with a margin of error so trivial that nobody cares.

Still: you ignore my point. Every scientific theory so far comes with a fine-print that we call 'domain of applicability' a.k.a context of validity.

2. Age's intellectual journey is still at its infancy. He is focused entirely on consistency. He pursues consistency religiously and idiomatically. He nitpicks at any and all inconsistencies - both small and big, to the point that if he were aware that Newton's equations were 'imprecise' he would insist that you used Einstein's equations - even here. On Earth even though the margin of error is insignificant.

He still has an all-or-nothing mindset. If it's not perfect it's junk.
Maybe we should wait to see how (s)he thinks. But it is just confusing the concern, given I read his discussion to Willy and was pointing out that the detail SEEMED odd to be concerned with when the specific (variable)constants change.

I'm not getting into Lorentz transformations here. I already spent way too much time finding superscripts to go further. You got the point.
uwot
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Re: Einstein on the train

Post by uwot »

Scott Mayers wrote: Wed Mar 20, 2019 4:11 pm I like your effort uwot and think it is necessarily lacking. I like the connectivity of it and have to ask which 'heroes' of science popularizers were your favorite?
Thank you. There's a few YouTube channels that I look at - Veritasium and Answers with Joe spring to mind. Richard Feynman was always brilliant. The Brian's and Carl Sagan are great. Paul Davis and Ian Gribben is going back a bit, but I read a lot of them. And yeah, I remember Connections, which is going back even further. My dad bought me the book of the series, which I still have, "as an antidote to Alice Cooper". Only partially successful-I've got tickets to see the old scrote this autumn. Anyone who knows what they are talking about and tries to make it accessible is worth listening to, in my view.
uwot
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Re: Einstein on the train

Post by uwot »

Logik wrote: Wed Mar 20, 2019 4:03 pmDepending on your position on Earth g is anywhere between 9.7639 m/s2, and 9.8337 m/s2
Which is 9.8 whichever way you round it up. As someone who provides a lot of links in your correspondence, I have to ask whether you have actually read the work that is the subject of this thread. I think you could save us all a lot of time if you were to stick to issues in that. https://willybouwman.blogspot.com
Logik
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Re: Einstein on the train

Post by Logik »

uwot wrote: Fri Mar 22, 2019 9:03 am
Logik wrote: Wed Mar 20, 2019 4:03 pmDepending on your position on Earth g is anywhere between 9.7639 m/s2, and 9.8337 m/s2
Which is 9.8 whichever way you round it up.
No, it's not!

Why did you CHOOSE to round UP to 9.8? Why didn't you CHOOSE to round UP to 10?
Why didn't you CHOOSE to round DOWN to 9.7 ? Or 9?

Decision theory, Mr Uwot... you ignore it.

uwot wrote: Fri Mar 22, 2019 9:03 am As someone who provides a lot of links in your correspondence, I have to ask whether you have actually read the work that is the subject of this thread. I think you could save us all a lot of time if you were to stick to issues in that. https://willybouwman.blogspot.com
As somebody who writes blogs about these things I wonder if you have ever actually used/applied the theory you write about, or if you have just read about it.

I have done both reading and application.

I think YOU will save us a lot of work if you recognize that all the issues I am pointing at are already embedded in your interpretation.
The way you frame the issue is incorrect. Your paradigm is incomplete.

Which is WHY you can't point out any problems in that which I am saying.
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

@ logik,

Just read it. You aren't required to agree to the particulars. I disagree with the Big Bang as the 'best explanation' but Willy's book is really well illustrated, has humor, and brings together everything better than I've seen in a while....all presented in a nice compressed but understandable format.

The 9.8 m/s² is the way you express mathematically the average acceleration due to gravity at the average sea level for Earth. You'd have to know how numbers are expressed in science. The '8' as the last digit is a 'guesstimate' as all the last digits in a measure are. That is why the scientific notation shows numbers in powers. It is NOT exact, just the average for a particular place as defined for gravity. Gravity differs by different masses used, different distances between the two, and this 'constant' is a "variable constant" if you want a comparison to computers.

If you want the actual constant look to my post above that explains what the ACTUAL fixed universal constant is and how you use the different factors of mass and distance with that to get the number for the local sea level average value of 9.8 m/s².
Logik
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Re: Einstein on the train

Post by Logik »

Scott Mayers wrote: Fri Mar 22, 2019 9:42 am @ logik,

Just read it. You aren't required to agree to the particulars. I disagree with the Big Bang as the 'best explanation' but Willy's book is really well illustrated, has humor, and brings together everything better than I've seen in a while....all presented in a nice compressed but understandable format.

The 9.8 m/s² is the way you express mathematically the average acceleration due to gravity at the average sea level for Earth. You'd have to know how numbers are expressed in science. The '8' as the last digit is a 'guesstimate' as all the last digits in a measure are. That is why the scientific notation shows numbers in powers. It is NOT exact, just the average for a particular place as defined for gravity. Gravity differs by different masses used, different distances between the two, and this 'constant' is a "variable constant" if you want a comparison to computers.

If you want the actual constant look to my post above that explains what the ACTUAL fixed universal constant is and how you use the different factors of mass and distance with that to get the number for the local sea level average value of 9.8 m/s².
I have read it. I have nothing against it - it makes current scientific knowledge more accessible to the masses. That's useful, but I am not its target audience.

The target audience of the blog is people who have neither theoretical nor practical grounding.

And so what people like me (who have theoretical and practical grounding) need to to is write a blog targeted at people like uwot who stand half way in between.

My point is merely that you have CHOSEN to round up 9.80665 m/s² to 9.8 m/s² where you could have CHOSEN to round it up to 10 m/s²

And since log2 ( 9.80665 ) = 3.293760388861827
You can basically round it down to 3, so 2^3 = 8
Or you can round it up to 2^3.3 = 9.9

That is what computer scientists call range-precision trade-off :)

Arbitrary choices everywhere...
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

Logik wrote: Fri Mar 22, 2019 10:17 am
Scott Mayers wrote: Fri Mar 22, 2019 9:42 am @ logik,

Just read it. You aren't required to agree to the particulars. I disagree with the Big Bang as the 'best explanation' but Willy's book is really well illustrated, has humor, and brings together everything better than I've seen in a while....all presented in a nice compressed but understandable format.

The 9.8 m/s² is the way you express mathematically the average acceleration due to gravity at the average sea level for Earth. You'd have to know how numbers are expressed in science. The '8' as the last digit is a 'guesstimate' as all the last digits in a measure are. That is why the scientific notation shows numbers in powers. It is NOT exact, just the average for a particular place as defined for gravity. Gravity differs by different masses used, different distances between the two, and this 'constant' is a "variable constant" if you want a comparison to computers.

If you want the actual constant look to my post above that explains what the ACTUAL fixed universal constant is and how you use the different factors of mass and distance with that to get the number for the local sea level average value of 9.8 m/s².
I have read it. I have nothing against it - it makes current scientific knowledge more accessible to the masses. That's useful, but I am not its target audience.

The target audience of the blog is people who have neither theoretical nor practical grounding.

And so what people like me (who have theoretical and practical grounding) need to to is write a blog targeted at people like uwot who stand half way in between.

My point is merely that you have CHOSEN to round up 9.80665 m/s² to 9.8 m/s² where you could have CHOSEN to round it up to 10 m/s²
And since rounding up is all about 50% error margins yo can just as well round up 9.8 to 18. It's still technically correct.

That is what computer scientists call range-precision trade-off :)

Arbitrary choices everywhere...
I think it is still relevant because even professional scientists more often than not lack the same means of communicating among each other with clarity. Writing science that is accessible is as much an art and the most 'ideal' form is such that is most universally understanding to all ages.

As to numbers, the first formal step in any science program and texts is to learn how and why you must treat measurements in science express itself to how precise its number is to that measure. 9.8 cannot be rounded to 18. Numbers are expressed as between 0 and 9 inclusive only and then you use powers of ten to express anything other than the first digit as a decimal. The last digit is the least significant one and is the only one that is 'rounded' up or down to the nearest decimal. So 9. 8 means 9.8 plus or minus 0.05.

Ten, 10 would be expressed as 1.0 x 10¹. But is only 'precise' to 0.5. That is less precise. 18 m/s² would be just false of the definition of a gravitational field acceleration rate at sea level without using some other measure other than the "m" for meters and "s" for seconds. Those units matter too in the expression.
Logik
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Re: Einstein on the train

Post by Logik »

Scott Mayers wrote: Fri Mar 22, 2019 10:41 am I think it is still relevant because even professional scientists more often than not lack the same means of communicating among each other with clarity.
ALMOST all scientists. Computer scientists have figured out how communication works.
How developing languages form nothing works.
We have strategies for navigating around ambiguity, semantics and all the tomfoolery that plagues human interaction.
We know how to transmit information from one human mind to another while there's so much noise in our communication mediums.
We know how to build consensus form near-zero shared knowledge.

We KNOW HOW to agree. IF you understand the rules of "The Game' e.g Turing completeness/Logic and a handful of basic algorithms/strategies for problem-solving.

https://en.wikipedia.org/wiki/Aumann%27 ... nt_theorem

I know how to apply this skill across disciplines IF the other party cooperates.
If they are non-cooperative, the same old 'people management' thing comes into play.

If you want to turn cooperation into a prisoners' dilemma then you will soon find out that you can't fame me.
I INSIST that you cooperate with me. Else it's war.
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Writing science that is accessible is as much an art and the most 'ideal' form is such that is most universally understanding to all ages.
It is most definitely an art, but it is also contingent. There will be plenty of people who will still not be able to make sense of it.

There is no such thing as 'universally accessible text'.
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am 9.8 cannot be rounded to 18.
Yes it can. IF you are working in base 18 with 1 bit precision everything is either 0 or 18.

This is fundamentally why the entire notion if 'truth' and 'falsity' is bullshit. It's a dichotomy. All dichotomies are nonsense.
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Numbers are expressed as between 0 and 9 inclusive
No. Those are not numbers. Those are digits. The above statement is ONLY true in the context of base 10 numeric system.

In the decimal system your alphabet for your digits is 0 to 9.
In a binary system the alphabet for your digits is 0 and 1
In an octal system the alphabet for your digits is 0 to 8
In a hexadecimal system the alphabet for your digits is 0 to 9, A,B,C,D,E,F

You take alphabets (language) for granted :)
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am only and then you use powers of ten to express anything other than the first digit as a decimal. The last digit is the least significant one and is the only one that is 'rounded' up or down to the nearest decimal. So 9. 8 means 9.8 plus or minus 0.05.
See! You have already made an error.

You take your digits for granted. I don't ;)
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Ten, 10 would be expressed as 1.0 x 10¹. But is only 'precise' to 0.5. That is less precise. 18 m/s² would be just false of the definition of a gravitational field acceleration rate at sea level without using some other measure other than the "m" for meters and "s" for seconds. Those units matter too in the expression.
Do you think you have a framework in which to quantify the concept of ''precision' without ending up in circularities?

The general form of 1.0 x 10¹ is: significant * base ^ exponent

10 = 1.0 x 10¹
11 = 1.1 x 10¹
16 = 1.6 x 10¹
20 = 2.0 x 10¹

Because 1.1 = 1 when you ROUND DOWN then it follows 10 = 11
BECAUSE 1.6 = 2.0 when you ROUND UP then it follows that 16 = 20

https://en.wikipedia.org/wiki/Floating-point_arithmetic
Scott Mayers
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Re: Einstein on the train

Post by Scott Mayers »

Logik wrote: Fri Mar 22, 2019 11:08 am
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am I think it is still relevant because even professional scientists more often than not lack the same means of communicating among each other with clarity.
ALMOST all scientists. Computer scientists have figured out how communication works.
How developing languages form nothing works.
How building consensus form near-zero shared knowledge works.

We KNOW HOW to agree.

https://en.wikipedia.org/wiki/Aumann%27 ... nt_theorem

I know how to apply this skill across disciplines IF the other party cooperates.
If they are non-cooperative, the same old 'people management' thing comes into play.

If you want to turn cooperation into a prisoners' dilemma then you will soon find out that you can't fame me.
I INSIST that you cooperate with me. Else it's war.
:twisted: Your destiny is my creation.
logik wrote:
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Writing science that is accessible is as much an art and the most 'ideal' form is such that is most universally understanding to all ages.
It is most definitely an art, but it is also contingent. There will be plenty of people who will still not be able to make sense of it.

There is no such thing as 'universally accessible text'.
There IS universal form, though.
logik wrote:
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am 9.8 cannot be rounded to 18.
Yes it can. IF you are working in base 18 with 1 bit precision everything is either 0 or 18.

And I clarified this point with the fact it can only stand with different units. The 9.8 is actually

[9.8 x 10⁰]Base 10 m/s²

You have to follow the agreed system of measures and languages. If you can't get the context yourself, then it is you who is making the mistake by missing the context of the expression for the "gravitational field constant of acceleration on Earth at the average sea level in this present century as measured in meters, seconds, and with base ten scalar."

Is it actually necessary to say all this if it is understood by default what is meant?

logik wrote:

This is fundamentally why the entire notion if 'truth' and 'falsity' is bullshit. It's a dichotomy. All dichotomies are nonsense.
CONTEXT. Truth is the 'agreement' identity between at least two people or between yourself and nature apart from yourself. Its 'context' includes the particular people in communication, the times, the places, the language spoken, etc. I don't get your concern other than that you are looking out of step with the ones you're speaking to.
logik wrote:
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Numbers are expressed as between 0 and 9 inclusive
No. Those are not numbers. Those are digits. The above statement is ONLY true in the context of base 10 numeric system.

In the decimal system your alphabet for your digits is 0 to 9.
In a binary system the alphabet for your digits is 0 and 1
In an octal system the alphabet for your digits is 0 to 8
In a hexadecimal system the alphabet for your digits is 0 to 9, A,B,C,D,E,F
:lol:
The number is the whole scalar (number minus the unit measures). The context is digits of course. Now you can look above to see my that I put the "base 10" for you there too so that you don't get confused.
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am only and then you use powers of ten to express anything other than the first digit as a decimal. The last digit is the least significant one and is the only one that is 'rounded' up or down to the nearest decimal. So 9. 8 means 9.8 plus or minus 0.05.
See! You have already made an error.

You take your digits for granted. I don't ;)
What mistake?

I'm very competent in computer logic and right down to the architecture level. The expressions were not needed for the expression of gravitation as it is understood by the context. If we were to continue this confusion, we'd have to keep questioning all our words until were back as children making sounds at each other to beg association of what we are trying to denote.
logik wrote:
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am Ten, 10 would be expressed as 1.0 x 10¹. But is only 'precise' to 0.5. That is less precise. 18 m/s² would be just false of the definition of a gravitational field acceleration rate at sea level without using some other measure other than the "m" for meters and "s" for seconds. Those units matter too in the expression.
Do you think you have a framework in which to quantify the concept of ''precision' without ending up in circularities?
18 m/s² is INACCURATE and IMPRECISE [just wrong.]
18.78033 m/s² is INACCURATE and PRECISE [the decimal points are precise but suggests you are off by 9, an error of accuracy (accounting error)]
9.78033 m/s² is both ACCURATE and PRECISE.
Logik
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Re: Einstein on the train

Post by Logik »

Scott Mayers wrote: Fri Mar 22, 2019 11:47 am ]There IS universal form, though.
All mathematicians disagree. All engineers also.

There is mathematical isomorphisms a.k.a functional equivalence.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am And I clarified this point with the fact it can only stand with different units. The 9.8 is actually

[9.8 x 10⁰]Base 10 m/s²
None of my feedback was about your units. it was about the meaning of 9 and 8.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am You have to follow the agreed system of measures and languages.
No, I don't. The part that Computer Scientists have mastered is to INVENT language/measurements/units on the fly.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am If you can't get the context yourself,
No. That's now how it works. All meaning IS contextual. And yet language is implicit, not explicit.

If we can't agree on the interpretative context that IS how ambiguity ensues.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am then it is you who is making the mistake by missing the context of the expression
Nope. Sorry - that's not how reality works ;)

if I can infer 10 different contexts from your words then I have an interpretative problem.
It's what linguists call Word Sense Disambiguation: https://en.wikipedia.org/wiki/Word-sense_disambiguation

Demonstration: I went to the bank yesterday. I spent 5 hours there.

That's not MY error. That's YOUR error. That you (incorrectly) assumed your words have a clear, concise and unambiguous meaning.

It's called the illusion of transparency.

Scott Mayers wrote: Fri Mar 22, 2019 11:47 am for the "gravitational field constant of acceleration on Earth at the average sea level in this present century as measured in meters, seconds, and with base ten scalar."

Is it actually necessary to say all this if it is understood by default what is meant?
You have missed my point ;)

Why have you rounded g up to 9.8 but NOT up to 10? Hmmm?
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am The number is the whole scalar (number minus the unit measures). The context is digits of course. Now you can look above to see my that I put the "base 10" for you there too so that you don't get confused.
You are still talking about Arithmetic. Arithmetic is just an algorithm to a computer scientist.

I am talking about an Alphabet. Language.

Mathematics is invented. It's just a language. And the rules of the language are as arbitrary as the rules of any grammar. Like English.

1+1 = 2, but i can invent you an arithmetic in which 1 + 1 = 3. it will take me some time, but I can.

And I promise you, it WILL produce theorems and it WILL be consistent.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am What mistake?
You take digits/numbers/arithmetic for granted.

I invent digits AND arithmetic from first principles in Computer Science.
Scott Mayers wrote: Fri Mar 22, 2019 11:47 am I'm very competent in computer logic and right down to the architecture level.
OK! So invent the digits and arithmetic from first principles.

1 + 1 means nothing UNTIL you define the meaning of +.
Scott Mayers wrote: Fri Mar 22, 2019 10:41 am 18 m/s² is INACCURATE and IMPRECISE [just wrong.]
18.78033 m/s² is INACCURATE and PRECISE [the decimal points are precise but suggests you are off by 9, an error of accuracy (accounting error)]
9.78033 m/s² is both ACCURATE and PRECISE.
See! I've triggered you - good. Means I've tripped over one of your cognitive dissonances.

Inaccuracy and imprecision are mathematically ISOMORPHIC from the perspective of a computer scientist.

If 9.78033 is accurate and precise, then 9.8 MUST BE inaccurate AND imprecise.

Because 9.78033 != 9.8 :)

But I am really REALLY glad that you have used the word 'wrong' to express your rage, because you are FINALLY making way to asking the question that I've wanted you to ask all along:

Can you separate Mathematics/logic from morality? No - you can't ;)

You can use g = 10, or g = 9.8, or g = 9.81 or g = 9.77 and you will get approximately correct answers every time. So why is that 'wrong'?
Last edited by Logik on Fri Mar 22, 2019 12:17 pm, edited 1 time in total.
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