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Messages - Tom Bishop

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6121
You are right. It also represents 15.21 days. 1/24th of a year is 15.21. It can also be interpreted like that. But division of this manner can also be interpreted on how many times the smaller number on the right fits into the bigger number on the left. The result should be a whole number.
WHY?! Why should it?
Why should the number of DAYS in a year divided by the number of HOURS in a day be a whole number?! They are completely different units.

The number of HOURS in a year divided by the number if HOURS in a day (if we are simplifying and assuming exactly 365 days and using that to calculate the number of hours in a year) will be a whole number because the unit is the same. But if you mix up the units you get a completely meaningless number.

I have already broken it out by hours. If you take a group of 24 days compared to the 365.24 day year, the number of hours in both is equivalent in ratio to 365.24 days / 24 hours.

Quote from: Tom Bishop
This is simple math.

A grouping of Twenty Four 24 hour days has 576 hours.

24 x 24 = 576

A year has 8765.76 hours in it.

365.24 x 24 = 8765.76

The ratio is 8765.76 hours / 576 hours

I am no longer using the year / day calculation.

Can we see if a grouping of Tewenty Four 24 hour days (576 hours) fits into a year that is 8765.76 hours long?

8765.76 hours / 576 hours = 15.21. No. It does not fit.

This is the same ratio as 365.24 / 24, and gives the same answer.

6122
This is simple math.

This is condescension

A grouping of Twenty Four 24 hour days has 576 hours.
24 x 24 = 576
A year has 8765.76 hours in it.
365.24 x 24 = 8765.76
The ratio is 8765.76 hours / 576 hours

What ratio? All you've done is divide the number of hours in a year by the number of hours in 24 days. Why would you do this?

Can we see if a grouping of Twenty Four 24 hour days (576 hours) fits into a year that is 8765.76 hours long?
8765.76 hours / 576 hours = 15.21. No. It does not fit.

So what? What does that prove?

This is the same ratio as 365.24 / 24, and gives the same answer.

Again, all you're doing with this calculation is deriving one twenty-fourth of a year. You're not deriving any 'ratio' between anything that needs to be ratioed. You're calculating that 1/24th of a year is 15.21 days.

You are right. It also represents 15.21 days. 1/24th of a year is 15.21. It can also be interpreted like that. But division of this manner can also be interpreted on how many times the smaller number on the right fits into the bigger number on the left. The result should be a whole number.

The rest of this thread seems to be just clarification about how division and ratios work, to check if the math of dividing years by days was correct.

... but you didn't divide years by days.

You've persistently divided 365.24 by 24  (days by hours) to arrive at a number of days that represents one twenty-fourth of a year (15.21).

We already know that a day of 24 hours doesn't fit exactly into a year of 365.24 days. The clue is in the 0.24. Otherwise the year  would be 365 days (365 sets of 24 hours), an exact number. Dividing this by 24 still gives one twenty-fourth of a year. This is why we have leap years. 

362.24 / 24 is equivalent in ratio to as if we broke this out by hours, as I wrote about on the previous page.

A Solar Day needs to fit exactly into a Solar Year of 365.24 days because the sun needs to be in the same place in the sky at that point. 12 PM Solar Noon at the start needs to end up at 12 PM Solar Noon at the end.

What are you trying to prove here Tom? That there isn't a whole number of days in one orbital year/period? We know this, hence leap year. That this somehow invalidates...something? How? Why? What? Why can't the rate of rotation NOT be an even ratio to the rate of orbit? What prevents this?

Look up the definition of a Solar Year. The sun needs to return to its same position. Solar Noon needs to be the same after a Solar Year.
Oh, awesome. We can /thread this then, because if you haven't noticed the equinoxes don't occur on the same day every year. Because our calendar system isn't defined by solar noons. In fact, solar noon for any location isn't even regular in time between them, due to variances in the Earths orbit and rotation mostly. See: https://www.timeanddate.com/astronomy/solar-noon.html Elastic Solar Noon.

If you try to use the amount of time the earth "actually rotates at" in relation to the stars, the Sidreal Day, it doesn't work either.

The Solar Year isn't based on the 365 day calendar. The Solar Year is ~365.24 days. Leap year is incorporated into the 365 day calendar to try and account for that.

6123
So are you saying that you believe the number of times the planet spins on its axis should fit into a single orbit the planet takes around the sun nice and neatly?

If so, then why do you feel this should be the case?

I genuinely don't get it.

Look into definitions of Solar Time and Solar Year and Solar Day. We have quoted them in this thread.

From https://en.wikipedia.org/wiki/Tropical_year --

Quote
A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

We looked at the real numbers earlier in this thread.

The rest of this thread seems to be just clarification about how division and ratios work, to check if the math of dividing years by days was correct.

What are you trying to prove here Tom? That there isn't a whole number of days in one orbital year/period? We know this, hence leap year. That this somehow invalidates...something? How? Why? What? Why can't the rate of rotation NOT be an even ratio to the rate of orbit? What prevents this?

Look up the definition of a Solar Year. The sun needs to return to its same position. Solar Noon needs to be the same after a Solar Year.

6124
The problem one might have with the above account with the MiniSlices, is why am I using the 365.24 / 24 at the end?

Well, that is the same ratio as if we multiplies both of those numbers by 24 and found the lowest common denominator.



1 Slice = 24 Minislices

365.24 x 24 = 8765.76
24 x 24 = 576

A ratio of 8765.76 / 576 is equivalent to 365.24 / 24.


8765.76 / 576 = 15.21

365.24 / 24 = 15.21
Tom, do you need to go lie down for a bit? You're honestly just spouting nonsense that's unrelated to any of the issues people are bringing up, and you still have yet to explain what you're attempting to prove/show here in any way. Your numbers are meaningless in context, and multiplying everything by 24 (or any number) doesn't show or solve anything.

This is simple math.

A grouping of Twenty Four 24 hour days has 576 hours.

24 x 24 = 576

A year has 8765.76 hours in it.

365.24 x 24 = 8765.76

The ratio is 8765.76 hours / 576 hours

I am no longer using the year / day calculation.

Can we see if a grouping of Tewenty Four 24 hour days (576 hours) fits into a year that is 8765.76 hours long?

8765.76 hours / 576 hours = 15.21. No. It does not fit.

This is the same ratio as 365.24 / 24, and gives the same answer.

6125
The problem you seem to have with the above account with the MiniSlices example, is why am I using the 365.24 / 24 at the end? Years and hours?

Well, that is the same ratio as if we multiplied both of the numbers by 24 and found the lowest common denominator.

1 Slice = 24 Minislices

365.24 x 24 = 8765.76 hours in the year
24 x 24 = 576 hours in 24 days (24 days picked because we need equivalence to the ratio)

A ratio of 8765.76 / 576 is equivalent to 365.24 / 24.

8765.76 / 576 = 15.21

365.24 / 24 = 15.21

Equivelent

6126
Continuing my last scenario:

1 Slice = 1 Day

Each Slice is divided into 24 smaller slices (lets call them MiniSlices)

We know that 1 Slice goes, allegedly, into a pie 365.24 times (Year)

We can do 365.24 / 1 to see if that works. The result is 365.24. Not a whole number. 1 Slice cannot fit a pie evenly.

-------------

We can also get rid of the concept of the single slice entirely and just focus on the MiniSlices.

We have 24 MiniSlices in the pie of equal length. Will they fit into the pie?

365.24 / 24 = 15.21. The answer is No. They will not fit.

6127
Not a random number.

The result isn't a "random number". The result is a ratio of how many times the second number fits into the first number.

Premise: We have a pie with really big slices. We have a Pie that is giant slice that takes up 50% of a possible 100%.

If we divide those, the equation 100 / 50 = 2.

Conclusion: Two is not a "random number". 50 fits into 100 two times perfectly. The pie can be filled with two of those equally sized slices.

--- --- ---

Premise: We have a pie with really big slices. We have a Pie that is giant slice that takes up 30% of a possible 100%.

If the pie is 30% filled, the equation is 100 / 30 = 3.333...

Conclusion: 3.333... means that 30% fills pie 3.333... times.

Conclusion: Since 3.333... times isn't a whole number, 30% isn't an even ratio if 100%

Conclusion: 30% does not work. The pie slice would actually need to fill the pie by 33.333...% to fit into the pie in equal slices.

6128
Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours.

No.

Divide 7 (days in a week) by 24 (hours) and you get 0.29166. So what? Does that mean weeks are wrong?

There is a rule in division that the larger group on the left side needs to be a bigger number than the smaller group on the right side for this to work.

7 / 24 = 0.29166  < --- This is not a valid equation for the purpose

If we change that around to "1 Day is 3 hours. Does a 3 hour day fit into a 6 day week?"
 
6 / 3 = 2. Whole Number. Works.

Does a 3 hour day fit into a 7 day week?

7 / 3 = 2.33. Not a whole number. A 3 hour day does not fit neatly into a week that is 7 days long. The earth has not finished rotating by the time it reaches that point.

6129
They aren't independent variables.

1 Year = 365.24 Days

24 hours = 1 Day

The related variable is Days.

The relationship isn't really any different than 100 pennies = 10 dimes, as demonstrated in my previous post.

The math doesn't need to know about the concept of money or rotations or years. The equation is a simple relationship ratio.

IF there are 24 hours in a day then it only fits into certain kinds of years. Visualize it.

Can a 24 hour day fit into a year that is 0.5 days long? NO

Can a 24 hour day fit into a year that is 2.5 days long? NO

The above examples should be easy to visualize. Very easy. The earth has not finished rotating by the time it reaches those points.

6130
If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?
If a Solar Day is how long it takes the earth to rotate on its axis.
And a Solar Year is how long it takes the earth to orbit the sun.

Why must the ratio of those be an integer? That implies that for every orbit the earth makes of the sun it rotates exactly 'x' times, and x is an integer.
Why should it be? The rotation speed (which, by the way, does change over time, very slowly) and orbit speed are determined by all kinds of things, there is no reason the ratio should be an integer.

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours. If this is true then the ratios must relate.

Imagine that we had a planet with a Solar Day that was a 10 hour day.

Imagine that that the Solar Year year of this planet was 100 days.

Lets define Solar Year as the time it takes for the Sun to return back to the same place in the sky in Solar Time. This means that each of the days in the year must be full rotations.

Does a Solar Day fit into a Solar Year?

100 / 10 = 10. Yes. A solar day fits into a Solar Year.

If we mess around those numbers, a solar day no longer fits into a Solar Year.

142 / 10 = 14.2. A solar day does not fit into a Solar Year.

100 / 7 = 16.6. A solar day does not fit into a Solar Year.

A result of a whole number shows that the second value fits into the first value. The only types of Years a 10 hour day would return whole numbers in such a division.

A 10 hour day can fit into a 10 day year (10 / 10 = 1), a twenty day year ( 20 / 10 = 2 ),  but not a 25 day year ( 25 / 10 = 2.5 ).

Each 10 doesn't fit nicely into the 25, and the result is 2.5. The Solar Days have not been completed by the time the planet makes its way to the end.

It doesn't make a difference if we call them planets and years or dimes and pennies. The relationship is defined and must be maintained.

Relationship: 100 pennies is 10 dimes. There are 10 pennies in a dime.

We have 142 pennies and 10 dimes. Does the relationship work?

142 pennies / 10 dimes = 14.2. This is not a whole number. 10 dimes does not fit into a value that is 142 pennies.

100 pennies / 7 dimes = 16.2. This is not a whole number. 7 dimes does not fit into a value that is 100 pennies.

10 dimes can fit into 10 pennies (10 / 10 = 1), 20 pennies (20 / 10 = 2), but it cannot fit into 25 pennies (25 / 10 = 2.5).

10 dimes doesn't fit nicely into the 25, and the result is 2.5.

6131
Sidrael Day is Star Time, and has nothing to do with this. What does it matter how fast the stars are moving in this?

Nobody is saying that it does matter. You seem to be manufacturing something to argue against.

Again, see https://en.wikipedia.org/wiki/Solar_time

References to a 'distant star' are merely as a reference point, a presumed stationary reference point ...

The stars move in the sky slightly slower than the sun. But this has nothing to do with the stars. Whatever you want to interpret about the stars and how the earth moves and where it is assumed to be fixed doesn't matter. In Solar Time the earth rotation is tied to the sun. If the stars disappeared from existence, Solar Time is still wrong.

Lets compare the smallest value to the largest value.

365.24162603 / 24.0000006 = 15.218400704

365.24274049 / 24.0000006 = 15.218447139

The difference isn't anywhere close to a whole number. This is way off.

Once again, you're a dividing an arbitrary number OF days by the number of hours WITHIN a day and expecting some correlation, when none is expected by anyone. ever.


As an aside;

The currency system in the UK used to be pounds, shillings and pence

1 pound = 20 shillings
1 shilling = 12 pence

You're doing the equivalent of

1 (pound) divided by 12 (pence) = 0.08333 .... oh, no, the currency system doesn't work (unless you divide 12 pounds by 12 pence, and get 1; or 24 pounds by 12 pence to get 2, 36 by 12 = 3, 48 by 12 = 4 ......) !

...

What are you talking about? Both of the values I am using involves days. 365.24 days in a Solar Year. 24 hours in a Solar Day. Each of those days in a Solar Year should have 24 hours in it.

We can see just by looking at the numbers that the 24 hour Solar Day won't fit into a 365.24 day year. The year has a decimal point at the end of it! But it's more than that. The closest kind of year a 24 hour Solar Day could fit into is if the earth had a 360 day year, or a 384 day year. A 365.24 day year does not make any sense.

From https://en.wikipedia.org/wiki/Tropical_year --

Quote
A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

The sun needs to return to the same position in the sky after one Solar Year.

This means that if Solar Noon starts over New York City at the beginning of the circuit, it needs to end with Solar Noon over New York City at the end of the circuit. As one example in the above quote shows, the Solar Time on Vernal Equinox needs to be the same as Vernal Equinox 1 and Vernal Equinox 2.

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

6132
I believe that I have shown a significant error in Solar Time, which is the heart of this discussion.

Lets define Tropical Year

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

Quote
A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

And the Topical Year varies on solar return points (which is why they called it the 'mean' tropical year):

http://calendars.wikia.com/wiki/Tropical_year

Quote
Current values and their annual change of the time of return to the cardinal ecliptic points[2] are:

    vernal equinox: 365.24237404 + 0.00000010338×a days
    northern solstice: 365.24162603 + 0.00000000650×a days
    autumn equinox: 365.24201767 − 0.00000023150×a days
    southern solstice: 365.24274049 − 0.00000012446×a days

Lets compare the smallest value to the largest value.

365.24162603 / 24.0000006 = 15.218400704

365.24274049 / 24.0000006 = 15.218447139

The difference isn't anywhere close to a whole number. This is way off.

6133
We learned earlier that a half year later, a sidereal day and a sun day are 12 hours apart. On one side of the sun they coincide, on the other side they are opposite. Since the only relationship that has changed is Earth to sun, the sidereal noon occurs at the same relative time that it did half a year ago, and solar noon now occurs 12 hours different. Oh wow, that makes solar noon continue to be during the day doesn't it? You're bringing in a requirement that doesn't exist and proclaiming it proves everything wrong. It's already been shown the difference between the two is 12 hours over the course of half of a year. Since the relative location of the stars to Earth doesn't change, that means the sun has done exactly what we experience every year. QED.

Sidrael Day is Star Time, and has nothing to do with this. What does it matter how fast the stars are moving in this?

Tumni has already settled the matter, by providing this link, right here:

The link Tumeni provided does say that Solar Day is technically "24.0000006 hours"

https://en.wikipedia.org/wiki/Day#Apparent_and_mean_solar_day

Quote
In recent decades, the average length of a solar day on Earth has been about 86 400.002 seconds (24.0000006 hours) and there are about 365.242 2 solar days in one mean tropical year.

Lets divide those numbers:

Solar Day: 24.0000006 hours
Year: 365.2422 Solar Days in a Year

Year / Day = 15.21842461953938

Oh no. This is not a whole number. Even with the more accurate numbers this doesn't work.

They put their contradiction right there in the same sentence, and even specified that it is Solar Days in both cases.

6134
We have 8 mysterious pieces of a pizza pie that are the same size and a pizza tray that holds 8 pieces.

We see that the two pieces make up 2/8th's of the pizza tray.

Can we calculate whether, if put in all 8 of the pizza slices (that are of the same size, if you recall above) of the pizza pie, would they fit?

8 / 2 = 4 -- Yes, these are whole slices that will all equally fit into the pizza tray. Tray divided by pizza slices. The result is a whole number. All 8 will fit.

2 / 8 = 0.25 -- This is not a valid equation for the purpose of this. Pizza slices divided by Tray? You need to put the larger numerical integer first to see if the smaller integer fits into it by producing a whole number.

6135
@Tom Bishop
Premises:
  • 1 day = 24 hours
  • 1 hours = 3600 seconds

1/2 day = 12 hours
12/3600 = 0.0033333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333(and so on) = not an integer

Oh no! Conclusion: seconds do not fit into 1/2 day  :o

Why are you placing the hours integer first when the goal is to see if seconds fits into hours?

You need to put in the numerically bigger number first if you are looking to see if the small number fits into it.

3600 / 12 = 300 = The ratio works. Whole number.

Conclusion: A second fits into an hour.

6136
The link Tumeni provided does say that Solar Day is technically "24.0000006 hours"

https://en.wikipedia.org/wiki/Day#Apparent_and_mean_solar_day

Quote
In recent decades, the average length of a solar day on Earth has been about 86 400.002 seconds (24.0000006 hours) and there are about 365.242 2 solar days in one mean tropical year.

Lets divide those numbers:

Solar Day: 24.0000006 hours
Year: 365.2422 Solar Days in a Year

Year / Day = 15.21842461953938

Oh no. This is not a whole number. Even with the more accurate numbers this doesn't work.

They put their contradiction right there in the same sentence, and even specified that it is Solar Days in both cases.

6137
Your Solar Day link says that the Solar Day is 24 hours long

The leap year happens because the year is 365.25636 days long. Why are you trying to use that as an explanation when that is already accounted for in the number.

6138
Sideral Noon is the fixed star's position. Yes, both images are facing us (the star). Congratulations. Sideral Noon changed.

But look at the picture! Solar Noon for NYC is different between both positions. NYC is in midnight in the bottom illustration. Uh oh. Solar Noon needs to be on the opposite side.

you're still not getting this.  just look at the image.  for the top bit, solar noon and sidereal noon are the same.  the star and the sun cross the local meridian at the same time.

for the bottom bit, sidereal noon happens at "solar midnight."  they're out of phase by twelve hours.  i genuinely do not understand what's troubling you about this geometry.

i think the problem is that you're assuming that over the course of an orbital period, a sidereal day and a solar day must have an integer ratio.  why must that be the case?

This is very easy to understand, Gary. I don't know why you are talking about the movement of the stars in relation to the sun. We are not talking about Star Time.

Lets break it down even simpler. Let not talk about half of the year. Lets talk about the full year. Very basic.

The Solar Time has a 24 hour cycle. That cycle does not fit into the length of the year of 365.25636 days.

Easy one, right? Just divide and we will get a whole number. But that is not what happens. The days don't fit.

6139
We don't know the number of hours in half a year in this problem.

.. but your premise to start with was

Premise:
     - A Solar Day happens every 24 hours
     - A Year happens every 365 days
365 days / 2 = 185.5 days in six months


So ....185.5 * 24 = 4452 hours.

The length of the earth's day doesn't fit into the year, whether whether we use 24 hours or 23.933333 hours (which is just star time, as we have read).

It doesn't work if we assume that the year is 365 days long or 365.25636 days long.

Please show how the number of days fits perfectly into the year.

This is very easy math.

We know that Solar Time has a 24 hour cycle. We know that the year is 365.25636 days long. How does it work?

6140
(...)
365.25636 / 2 = 182.62818 days in six months
(...)

Which six months? The year isn't divided evenly... (and there's reason for it)

But it doesn't matter if the movement of the earth around the sun is not a perfect circle. We are concerned solely with with ratios. The illustration is of Vernal and Autumnal Equinox.

Sidrael Time is star time, not the day and night time, and if that is the definition then I don't see why we should use it in this at all.

it's clear you simply don't fully understand the model you're criticizing.



i added a star to show you how these are related.  at the top, solar noon and "sidereal noon" are the same.  at the bottom, solar noon and sidereal noon are 12 hours apart.

Sideral Noon is the fixed star's position. Yes, both images are facing us (the star). Congratulations. Sideral Noon (star time) changed.

But look at the picture! Solar Noon for NYC is different between both positions. NYC is in midnight in the bottom illustration. Uh oh.

It appears that Star Time is not what we want to talk about here, and the rate the stars move in respect to the sun are not directly relevant. Why should we be concerned with the movement of the stars when we are talking about Solar Noon?

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