Did Issac Newton know about numeral systems?

[CuriosOne]

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? 

If not then, why do we use them "in calculus today??" 

Moreover, how can computers compute calculus? Issac Newton didn't have one, or did he?? Was it a Macintosh??  seriously..

This should be a very interesting thread..

Edited December 13, 2020 by CuriosOne

[Endy0816]

2 hours ago, CuriosOne said:

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? 

If not then, why do we use them "in calculus today??" 

Moreover, how can computers compute calculus? Issac Newton didn't have one, or did he?? Was it a Macintosh??  seriously..

This should be a very interesting thread..

We've used a variety of bases as a species historically. Base 20, base 8, base 12. Just depended how people wanted to count on their fingers and toes. Newton would have been familiar with the concept.

Logarithms are used in the change-of-base formula. Not strictly necessary to figure it out though. You could always just count or work it out in your head.

Computers do math the same as you and I might.  Newton probably used an Abacus though(which more or less involve some of that converting themselves).

Edited December 13, 2020 by Endy0816

[Sensei]

3 hours ago, CuriosOne said:

If not then, why do we use them "in calculus today??" 

No. We don't use "numeral systems in calculus"...

Numeral system is just a way to display numbers..

3 hours ago, CuriosOne said:

Moreover, how can computers compute calculus?

1) computers don't compute calculus by themselves. They execute program written in machine code.

2) computers are programmable, so programmer is responsible for making code which is doing something the programmer wants.

3) computers have just a basic set of math instructions. Add, subtract, multiply, divide, and, or, xor, not, sin, cos. Nothing complex.

Actually, you don't need to have multiply, divide, sin or cos instructions in CPU at all. Old CPUs (e.g. Motorola 6502/6510) did not have them, but programmer still could simulate these operations.

4) you don't need computer to compute by yourself.

3 hours ago, CuriosOne said:

Issac Newton didn't have one, or did he?? Was it a Macintosh??  seriously..

He had a brain... and a sheet of paper... and a pencil...

3 hours ago, CuriosOne said:

This should be a very interesting thread..

Doubtful.

 

Edited December 13, 2020 by Sensei

[joigus]

7 hours ago, CuriosOne said:

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? 

Oh, base 1. What a great idea.

[swansont]

52 minutes ago, joigus said:

Oh, base 1. What a great idea.

It's real

https://en.wikipedia.org/wiki/Unary_numeral_system

 

In the original use of the word, a "computer" was a person who did computations. That died out as mechanical and then electronic machines were developed to do these things. I'm not sure what computations Newton would have been doing. Calculus uses functions, and a lot of work can be done without doing any computations (i.e. no number manipulation)

[joigus]

10 minutes ago, swansont said:

It's real

https://en.wikipedia.org/wiki/Unary_numeral_system

 

In the original use of the word, a "computer" was a person who did computations. That died out as mechanical and then electronic machines were developed to do these things.

Interesting. Thank you. Although this is not a "base", "digits", and "place-holding" system AFAICS.

I mean, not based on powers of the base for place holding, but on addition of the digit, so to speak.

But very interesting anyway.

[John Cuthber]

Newton grew up in a world where 12 inches made a foot, three feet made a yard, Two yards (or six feet) made a fathom,  five and   a half yards made a pole, four poles made a chain; ten chains made a furlong and 8 furlongs made a mile.
He would have measured masses: 16 drachms made 1 ounce, 16 ounces made 1 pound and 14 pounds made a stone. Two stone was a quarter and 4 quarters (112 pounds)  made a hundredweight and 20 hundredweight made a ton.
 

He was, for a while, Master of the Mint so he understood that you got four farthings to the penny, 12 pennies to a shilling and 20 shillings to the pound. He also knew about guineas (twenty-one shillings).

He must, therefore, have been able to do arithmetic in bases 3,4,5.5,6, 8, 10, 12, 14 ,16 20 and 21.

You can add 60 to the list, since he will have worked in minutes and seconds (of arc and of time).

Given that he was bright and numerate, he would probably been able to figure in gross (144) too.

His published works would have included the Roman and Arabic numeral systems.

 

So why would the question "Did Issac Newton know about numeral systems?" lead to
 

9 hours ago, CuriosOne said:

a very interesting thread.

?
The answer is obviously "yes".
A batter question might be "will we ever teach "CuriousOne" about number bases?"

 

[CuriosOne]

1 hour ago, John Cuthber said:

Newton grew up in a world where 12 inches made a foot, three feet made a yard, Two yards (or six feet) made a fathom,  five and   a half yards made a pole, four poles made a chain; ten chains made a furlong and 8 furlongs made a mile.
He would have measured masses: 16 drachms made 1 ounce, 16 ounces made 1 pound and 14 pounds made a stone. Two stone was a quarter and 4 quarters (112 pounds)  made a hundredweight and 20 hundredweight made a ton.
 

He was, for a while, Master of the Mint so he understood that you got four farthings to the penny, 12 pennies to a shilling and 20 shillings to the pound. He also knew about guineas (twenty-one shillings).

He must, therefore, have been able to do arithmetic in bases 3,4,5.5,6, 8, 10, 12, 14 ,16 20 and 21.

You can add 60 to the list, since he will have worked in minutes and seconds (of arc and of time).

Given that he was bright and numerate, he would probably been able to figure in gross (144) too.

His published works would have included the Roman and Arabic numeral systems.

 

So why would the question "Did Issac Newton know about numeral systems?" lead to
 

?
The answer is obviously "yes".
A batter question might be "will we ever teach "CuriousOne" about number bases?"

 

So from what I see, a base is "any number" 

So if the base is 10

10^2 = 100 or 1

Or 10, 20, 30, 40 etc ??

So if the base is 3

3^2 = 9 or again 1

Or 3, 6, 9, 12,  etc ??

And where did that 2 come from??

The one in 10^2 <---

The one in 3^2<---

 

 

 

8 hours ago, Sensei said:

No. We don't use "numeral systems in calculus"...

Numeral system is just a way to display numbers..

1) computers don't compute calculus by themselves. They execute program written in machine code.

2) computers are programmable, so programmer is responsible for making code which is doing something the programmer wants.

3) computers have just a basic set of math instructions. Add, subtract, multiply, divide, and, or, xor, not, sin, cos. Nothing complex.

Actually, you don't need to have multiply, divide, sin or cos instructions in CPU at all. Old CPUs (e.g. Motorola 6502/6510) did not have them, but programmer still could simulate these operations.

4) you don't need computer to compute by yourself.

He had a brain... and a sheet of paper... and a pencil...

Doubtful.

 

So "where" does sin, cos and tan come from?  "as they" are a table of values among itself, and without it trigonometry "numbers" the results of the triginometry fractions are useless..I'm glad to know "highly relied on" machines, use "simple" math concepts...Maybe nature is simpler than I thought.

8 hours ago, Sensei said:

No. We don't use "numeral systems in calculus"...

Numeral system is just a way to display numbers..

1) computers don't compute calculus by themselves. They execute program written in machine code.

2) computers are programmable, so programmer is responsible for making code which is doing something the programmer wants.

3) computers have just a basic set of math instructions. Add, subtract, multiply, divide, and, or, xor, not, sin, cos. Nothing complex.

Actually, you don't need to have multiply, divide, sin or cos instructions in CPU at all. Old CPUs (e.g. Motorola 6502/6510) did not have them, but programmer still could simulate these operations.

4) you don't need computer to compute by yourself.

He had a brain... and a sheet of paper... and a pencil...

Doubtful.

 

How on earth does calculus not use numeral systems if its trigonometry based??

IE Secants, Tangent "Lines"

These are straight lines, they "don't bend." 

 

Edited December 13, 2020 by CuriosOne

[Sensei]

11 minutes ago, CuriosOne said:

So "where" does sin, cos, and tan come from?  "as they" are a table of values among itself, and without it trigonometry is useless..I'm glad to know "highly relied on" machines, use "simple" math concepts...Maybe nature is simpler than I thought.

sine alpha = b/c

cosine alpha = a/c

Tables can be used. They speed up calculations. Tables were used frequently in the 1980s and 1990s for trigonometry before FPUs were introduced to processors.

But there are algorithms which simulate sin/cos without having to rely on tables.

Obviously you can find detailed descriptions of algorithms on.. Wikipedia..

https://en.wikipedia.org/wiki/Sine

 

 

[CuriosOne]

1 minute ago, Sensei said:

sine alpha = b/c

cosine alpha = a/c

Tables can be used. They speed up calculations. Tables were used frequently in the 1980s and 1990s for trigonometry before FPUs were introduced to processors.

But there are algorithms which simulate sin/cos without having to rely on tables.

Obviously you can find detailed descriptions of algorithms on.. Wikipedia..

https://en.wikipedia.org/wiki/Sine

 

 

What Base Does It Use???

For, Sin, Cos, Tan...?

Edited December 13, 2020 by CuriosOne

[Sensei]

1 minute ago, CuriosOne said:

What Base Does It Use???

For, Sin, Cos, Tan...?

It is not important. It can be any base. Any numerical system.

[MigL]

We use base 10 for the probable reason that we can count on ten fingers.
Computers use base 2 because they can only count on two fingers ( voltage on, and voltage off ).
But you can represent any number or math operation in either base.

 A simple way of looking at base is the number of digits you use.
Base 10 uses 10 digits, 0,1,2...8,9.
Base 2 use only two digits, o and 1 ( voltage on, and voltage off ).

[CuriosOne]

3 minutes ago, Sensei said:

It is not important. It can be any base. Any numerical system.

Are You 100% Sure On This??

4 minutes ago, MigL said:

We use base 10 for the probable reason that we can count on ten fingers.
Computers use base 2 because they can only count on two fingers ( voltage on, and voltage off ).
But you can represent any number or math operation in either base.

 A simple way of looking at base is the number of digits you use.
Base 10 uses 10 digits, 0,1,2...8,9.
Base 2 use only two digits, o and 1 ( voltage on, and voltage off ).

Understood but:

Counting by base 10= 10, 20, 30 

Counting by base 2 = 2, 4, 6

Is this correct?

[Sensei]

...I am waiting for somebody training his/her computer chatbot on science forums... I imagine discussion will be as "fruitful" as this one...

 

 

[CuriosOne]

15 minutes ago, Sensei said:

...I am waiting for somebody training his/her computer chatbot on science forums... I imagine discussion will be as "fruitful" as this one...

 

 

Stop diverging my "question" its ok if you do not know the answer and please refrain the awkward and bizarre philosophy its not working with me anymore...

With this said,  its hard to believe that trigonometry can be used with any base numeral system when considering "magnatude and direction" acceleration and all other angle based relationships in regards to time...

Edited December 13, 2020 by CuriosOne

[swansont]

37 minutes ago, CuriosOne said:

Are You 100% Sure On This??

The equations do not indicate that any particular base must be used. 

We do in in base 10 when we calculate by hand. Computers do it in base 2 when they calculate. The answers are the same. 

Can you give a legitimate reason to expect otherwise?

13 minutes ago, CuriosOne said:

Stop diverging my "question" its ok if you do not know the answer and please refrain the awkward and bizarre philosophy its not working with me anymore...

With this said,  its hard to believe that trigonometry can be used with any base numeral system when considering "magnatide and direction" acceleration and all other angle based relationships... 

What angle relationships incorporate direction?

Acceleration is dv/dt. There’s no inherent angle-based relationship.

I think one of your difficulties is that you are unable to draw distinctions between independent areas of math and science.

43 minutes ago, CuriosOne said:

Understood but:

Dubious claim, given the evidence.

43 minutes ago, CuriosOne said:

Counting by base 10= 10, 20, 30 

Counting by base 2 = 2, 4, 6

Is this correct?

For base n, the digits from right to left are n^0, n^1,n^2, etc.

i.e. for base 10, it’s 1, 10 (10^1), 100 (10^2), etc.

123 in base 10 is one hundred, two tens (i.e. twenty) and 3 ones

 

If I instead chose base 8, 123 would represent one 64 (8^2), two eights, and three ones. 123 in base 8 is equal to 83 in base 10

 

[CuriosOne]

19 minutes ago, swansont said:

The equations do not indicate that any particular base must be used. 

We do in in base 10 when we calculate by hand. Computers do it in base 2 when they calculate. The answers are the same. 

Can you give a legitimate reason to expect otherwise?

What angle relationships incorporate direction?

Acceleration is dv/dt. There’s no inherent angle-based relationship.

I think one of your difficulties is that you are unable to draw distinctions between independent areas of math and science.

Correct I do not see them in algebrea they appear to be angle based..

For instance I've seen acceleration expressed as v1-v2 = some distance then I see that same distance / some change in time...

But "where in time"  is what I do not comprehend...

Let's also note that "accelerations" is "relative" ie the moon "falling around earth" or radio signals bouncing off walls at a certain time dt, it would help if we mention this as "detection" disturbances or simply observations..All of coarse are created through some "physical force."

You may see how all this confuses anyone when onto of this computers, people and even atoms for that matter decide to use their own number systems... 

Edited December 13, 2020 by CuriosOne

[studiot]

1 hour ago, CuriosOne said:

So from what I see, a base is "any number" 

So if the base is 10

10^2 = 100 or 1

Or 10, 20, 30, 40 etc ??

So if the base is 3

3^2 = 9 or again 1

Or 3, 6, 9, 12,  etc ??

And where did that 2 come from??

The one in 10^2 <---

The one in 3^2<---

 

I'm disappointed that is all you have to say about John Cuthber's useful and bang on topic answer (+1 John).

That said, if you really don't know the answer to these questions you have made do you know what onethousand and one looks like ?

Can you write it down ?

 

To add to John's and swansont's comments

 

4 hours ago, swansont said:

I'm not sure what computations Newton would have been doing. Calculus uses functions, and a lot of work can be done without doing any computations (i.e. no number manipulation)

Not only did Newton invent the differential calculus (which has no relevence to this thread) he also invented the calculus of finite differernces, which does.

Finite differences are vital to constructing and using tables of numerical values (in whatever base you choose) as before artificial devices were made to do the this work they were the only way to calculate.
Obviously someone had to work out these tables in the first place and Newton was the boy that made it possible.

It is also disappointing that you are running round again spinning off question threads without ever dealing with or properly absorbing the answers.

Slow down and catch yourself up.

[joigus]

8 minutes ago, CuriosOne said:

Let's also note that "accelerations" is "relative" ie the moon "falling around earth" or radio signals bouncing off walls at a certain time dt, it would help if we mention this as "detection" disturbances or simply observations..

There is no chance that you can get it right, even by mistake. Acceleration in Galilean relativity is not relative. It's actually what all inertial observers agree upon, so it's a more invariant concept than velocity or position. In Einstein's relativity it's more involved, although you can generalise the concept by introducing proper time, but look who I'm talking too.

What that has to do with OP, Newton and bases is anybody's guess.

Edited December 13, 2020 by joigus

[swansont]

4 minutes ago, CuriosOne said:

Correct I do not see them in algebrea they appear to be angle based..

For instance I've seen acceleration expressed as v1-v2 = some distance then I see that same distance / some change in time...

But "where in time"  is what I do not comprehend...

Let's also note that "accelerations" is "relative" ie the moon "falling around earth" or radio signals bouncing off walls at a certain time dt, it would help if we mention this as "detection" disturbances or simply observations..All of coarse ate created through some "physical force."

You may see how all this confuses anyone when onto of this computers, people and even atoms for that matter decide to use their own number systems... 

“I think one of your difficulties is that you are unable to draw distinctions between independent areas of math and science.” (me, above)

Case in point. We were discussing trig (at that point, at least. Your threads do tend to meander)

None of what you said here is trig. You’ve mashed velocity, acceleration, physical forces, atomic theory and number systems together. I think someone with expertise on cognition might have some insight here on your tendency to do this. I, however, am at a loss.

[iNow]

57 minutes ago, Sensei said:

I am waiting for somebody training his/her computer chatbot on science forums...

IMO, we’ve been seeing several of these already over the past few weeks

[CuriosOne]

18 minutes ago, iNow said:

IMO, we’ve been seeing several of these already over the past few weeks

Who's We?? The collective conscious?

🤣😂🤣😂🤣😂🤣🤣😂🤣😂🤣🤣🤣

[iNow]

4 minutes ago, CuriosOne said:

Who's We??

This community, the forum where you’ve been posting 

[CuriosOne]

42 minutes ago, swansont said:

“I think one of your difficulties is that you are unable to draw distinctions between independent areas of math and science.” (me, above)

Case in point. We were discussing trig (at that point, at least. Your threads do tend to meander)

None of what you said here is trig. You’ve mashed velocity, acceleration, physical forces, atomic theory and number systems together. I think someone with expertise on cognition might have some insight here on your tendency to do this. I, however, am at a loss.

Wait a moment here...

Calculus is very advanced algebra and geometry, that uses a ratio "ie" derivative between at least 2 "observations." In other words its trigonometry based.

"Unless of coarse" its pi based, another word for tri based...What ever it is at this point it's truly a mixture of things..

13 minutes ago, iNow said:

This community, the forum where you’ve been posting 

So you speak for everyone right??

Its called:

P O L I T I C A L  C O R R E C T N E S S

36 minutes ago, iNow said:

IMO, we’ve been seeing several of these already over the past few 

Stop cyber bullying me...and stop instigating others to make fun of my posts..

Edited December 13, 2020 by CuriosOne

[Sensei]

34 minutes ago, iNow said:

IMO, we’ve been seeing several of these already over the past few weeks

Chatbots don't understand meaning of words or digits, sarcasms. They don't think abstractly. Can't read and understand Internet articles etc etc.