# Debunked: Rivers flow uphill

#### Ion

##### New Member
I understand the calculation - I did it myself in the OP - but what I'm curious about is what you think is wrong with the source of the Mississippi being around 6000 metres further from the centre of the earth than its mouth?

See the answer for Trailblazer. As much time as r1-r2 is a positive number, the Mississippi is flowing uphill. I am not allowed to introduce an acceleration like that from the spinning of the Earth because that would result in water speeds which are not matched by reality. It is much easier to change the geodedic systems.

#### Z.W. Wolf

##### Senior Member.
If I'm reading this correctly you're insisting that earth radius is the only important factor. I'm asking you to go back to Isaac Newton's thought experiment as presented earlier.

#### Z.W. Wolf

##### Senior Member.
I am not allowed to introduce an acceleration like that from the spinning of the Earth because that would result in water speeds which are not matched by reality. It is much easier to change the geodedic systems.

What have you calculated?

#### Ion

##### New Member
Rivers go downhill, taking the path of least resistance. The Mississippi just happens to go south. The Rhine in Europe and The Nile in Africa both spend most of their courses going in a Northerly direction towards the North Sea and the Mediterranean respectively. In South America the Amazon and The Orinoco both head East towards the Atlantic, while going back to Africa the Congo flows mainly in a westerly direction, again to Atlantic. Its all down to gravity and the path of least resistance, the spinning of the earth has nothing to do with it.

The gravity is toward the center of the Earth and r1-r2 difference exceeds six thousands meters, r1 beeing the Earth radii at the Mississippi mouth latitude and r2 beeing the Earth radii at the Itasca lake latitude.

#### Rory

##### Senior Member.
The gravity is toward the center of the Earth and r1-r2 difference exceeds six thousands meters, r1 being the Earth radii at the Mississippi mouth latitude and r2 being the Earth radii at the Itasca lake latitude.
Right. You keep saying that, and no one's disagreeing with you - that's all accepted, and isn't a problem.

But I presume there's a point?

#### Ion

##### New Member
If I'm reading this correctly you're insisting that earth radius is the only important factor. I'm asking you to go back to Isaac Newton's thought experiment as presented earlier.

I fully agreed with your thought experiment, but it does not answer my question. I do not agreed with the flat Earth solution because the sun seems to go up when it rise instead to come to me. Also the horizon line is ascending if I am going upside. The sun has to be much bigger at noon and so on. But the round Earth is not without faults: take a point in Africa on the equator today at noon. After 30 days multiplied by 6 months, which is 180 days, in the same point has to be around midnight, because the Earth is spinning once at every 24 hours. That does not happen in reality.

The problem in your thought experiment is that we do not have a force to push the Mississippi volume along the r1-r2 difference, where r1 is the Earth radii at the Mississippi mouth latitude and r2 is the Earth radii at the Itasca lake latitude.

#### Ion

##### New Member
What have you calculated?

I met this flowing uphill problem on a flat earth forum or site and I wanted to check. I took the formula for the Earth radii by latitude from wikipedia.org and I calculate r1 and r2. Our geodedic systems are not good, we cannot invent an other math.

#### Z.W. Wolf

##### Senior Member.
After 30 days multiplied by 6 months, which is 180 days, in the same point has to be around midnight, because the Earth is spinning once at every 24 hours. That does not happen in reality.

This is a misunderstanding of the difference between solar days and sidereal days which I have run into many times. But that's an issue for a separate thread.

#### Z.W. Wolf

##### Senior Member.
The problem in your thought experiment is that we do not have a force to push the Mississippi volume along the r1-r2 difference, where r1 is the Earth radii at the Mississippi mouth latitude and r2 is the Earth radii at the Itasca lake latitude.

#### Ion

##### New Member
Right. You keep saying that, and no one's disagreeing with you - that's all accepted, and isn't a problem.

But I presume there's a point?

See my #41 answer for you and the anwer for Trailblazer. Our geodedic systems are wrong.

#### Rory

##### Senior Member.
The round Earth is not without faults: take a point in Africa on the equator today at noon. After 30 days multiplied by 6 months, which is 180 days, in the same point has to be around midnight, because the Earth is spinning once at every 24 hours. That does not happen in reality.
There's a thread on here dealing with that question - common misunderstanding.

https://www.metabunk.org/explained-flat-earth-theory-why-don’t-our-clocks-have-to-change-by-12-hours-in-6-months.t7193/
See my #41 answer for you and the answer for Trailblazer. Our geodedic systems are wrong.
Your 'answer' to Trailblazer mentioned something to do with the ocean floors - which I presumed was either a typo or a joke. As far as I can see, you still haven't really said anything, other than that the "geodedic [sic] system is wrong." But to progress with that, you'll either have to demonstrate why; or, perhaps more wisely, read the thread again and try to understand the explanations. I know it's perhaps a little difficult to get one's head around - somewhat counterintuitive, really - but you'll get there in the end.

PS It's "geodetic", not "geodedic."

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#### Ion

##### New Member

I did not have a work, but I could take again the wikipedia formula and calculate here.

#### Z.W. Wolf

##### Senior Member.
What I'm asking for is not another measurement of earth radius, you understand. I'm asking how you came to the conclusion...
... that we do not have a force to push the Mississippi volume along the r1-r2 difference, where r1 is the Earth radii at the Mississippi mouth latitude and r2 is the Earth radii at the Itasca lake latitude.

Why have you decided that we do not have a [n adequate] force to "push" the Mississippi along... etc.? Where are your calculations?

#### Clouds Givemethewillies

##### Senior Member
You are being a bit pedantic there. We know F = ma, and we know things don’t fly off into space. So for any given object the force due to gravity is more than the effective force due to the earth spinning. We don’t need more for the purposes of this thread.
I won't ask for a value for gravity on Earth using poundals, then.

#### Ion

##### New Member
I am on a tablet and I do not have greek alphabet letters. So the rXX will be the Earth radius at XX latitude. The formula is

rXX = square root[[(a squared plus cos XX)squared plus (b squared sin XX)squared]/[(a multiplied cos XX)squared plus (b multiplied sin XX)squared]]

where a is the equatorial radius and b is the polar radius. Is that good enough?

#### Ion

##### New Member
Romanian post released a parcel which came from China at the end of August. I have to go for a few hours.

#### Rory

##### Senior Member.
I am on a tablet and I do not have greek alphabet letters. So the rXX will be the Earth radius at XX latitude. The formula is

rXX = square root[[(a squared plus cos XX)squared plus (b squared sin XX)squared]/[(a multiplied cos XX)squared plus (b multiplied sin XX)squared]]

where a is the equatorial radius and b is the polar radius. Is that good enough?
Not really. We already know that, as the same calculation was done in the very first post, with the same result.

Nobody is disputing this figure, nor the formula for it. The question you're being asked is:
Why have you decided that we do not have a[n adequate] force to "push" the Mississippi along... etc.? Where are your calculations?

#### Trailblazer

##### Moderator
Staff member
See the answer for Trailblazer. As much time as r1-r2 is a positive number, the Mississippi is flowing uphill. I am not allowed to introduce an acceleration like that from the spinning of the Earth because that would result in water speeds which are not matched by reality. It is much easier to change the geodedic systems.
The Earth's radius is irrelevant. What matters is the height relative to sea level. Sea level is higher at the equator (relative to the centre of the Earth) than it is at the pole. Therefore a river can get further from the centre of the Earth as it heads towards the equator and still be flowing downhill!

I haven't looked up the actual figures, but let's simplify:

Distance from centre of earth to sea level at latitude of river source = S

Distance from centre of earth to sea level at latitude of mouth = S + X

Distance from centre of Earth to river source = R

Distance from centre of Earth to river mouth = R + Y, which = S + X because the mouth is at sea level.

Y and X are independent of each other.

This needs a diagram.

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#### Trailblazer

##### Moderator
Staff member
Here's an attempt at a diagram to show what I mean. If you look at the grey dotted circle you can see that the mouth of the river is further from the centre of the Earth than the source is. However, if you compare them to the blue ellipse of sea level, you can see that the mouth is lower than the source.

Obviously the flattened shape of the Earth (and the height of the source above sea level) is vastly exaggerated here. What is important is that we measure heights above sea level, and the dotted line (the distance from the centre of the Earth) is irrelevant to that.

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#### Z.W. Wolf

##### Senior Member.
I'm afraid that people who aren't used to thinking in terms of potential energy just aren't going to understand this.

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#### cloudspotter

##### Senior Member.
Let's see if I've got this right. The Mississippi is flowing uphill but since the force that creates that uphill acts on everything (crust, sea, river) the same then the uphill is effectively cancelled out?

#### Ion

##### New Member
The romanian post release a parcel at noon and the custom from that post office is closing three hours later! I shall go tomorrow.

First I thanks to Rory for the message with the link to the thread in which Mick West explain that the daily difference caused by orbit around the sun is included in the twenty four hours, so I understood that I was wrong with "the point in Africa" from post #46!

Now back to topic at the nice diagram of Trailblazer. My understanding is that if I calculate r1 beeing the Earth radii at the mouth of Mississippi latitude, R+Y from Trailblazer explanation, I should stand on the blue ellipse because the Earth bulge contain the floor of the Gulf of Mexico also. So, from the point of view of an observer which is looking at me from the shore of the Itasca lake above the r2 Earth radii from that latitude, I cannot be downhill as I am more than six kilometers above his altitude.

The fact that the observer from the Itasca lake is at a r2+450 meters altitude does not help me. He is still at a lower distance from the center of the Earth and all the Mississippi waters between us should flow toward him not toward me. What I am missing?

#### Trailblazer

##### Moderator
Staff member
Let's see if I've got this right. The Mississippi is flowing uphill but since the force that creates that uphill acts on everything (crust, sea, river) the same then the uphill is effectively cancelled out?
Not really. Or rather, technically yes, but not really helpful IMHO. It's more that the notion of "uphill or downhill" is not dependent (solely) on the distance from the centre of the Earth.

The Mississippi doesn't flow "uphill" because we DEFINE downhill to be "in the direction that things naturally fall". That's what downhill means.

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#### Trailblazer

##### Moderator
Staff member
The fact that the observer from the Itasca lake is at a r2+450 meters altitude does not help me. He is still at a lower distance from the center of the Earth and all the Mississippi waters between us should flow toward him not toward me. What I am missing?

You are missing the fact that waters flow towards sea level. That's why sea level is sea level: it's the lowest point that water can flow to! The distance from the centre of the Earth is irrelevant. Forget the distance from the centre of the Earth.

#### Trailblazer

##### Moderator
Staff member
Here, let me remove the dotted circle from my diagram, since it seems to be causing confusion.

The blue ellipse (sea level) represents a surface that has the same potential energy. Anything above (i.e. outside) this blue ellipse has higher potential energy, so when released it will fall to sea level. So what will happen to a raindrop falling on the top of the green mountain?

#### Ion

##### New Member
You are missing the fact that waters flow towards sea level. That's why sea level is sea level: it's the lowest point that water can flow to! The distance from the centre of the Earth is irrelevant. Forget the distance from the centre of the Earth.

I do not know how to cancel a reply to a post, so I think this answer will appear above new diagram of the Trailblazer, that without the dotted circle (post #66).

In my understanding the sea level cannot be below the Gulf of Mexico floor and, as the Gulf of Mexico floor in included in r1, which is higher than r2 with more than six kilometers, the Mississippi cannot flow toward a sea level which is more than six thousand meters higher than its source.

I think that the green line is wrong drawed as there is no mountain between the Itasca lake and the Gulf of Mexico. Why did you say that I am missing the sea level?

#### Ion

##### New Member
I'm afraid that people who aren't used to thinking in terms of potential energy just aren't going to understand this.

Potential energy is Ep=mgh, where Ep is potential energy, m the mass of the object, g the acceleration of gravitation and h the altitude. We are not agreeing on h.

I do not know how you are noting potential energy in english books, so I used my high school simbols. In romanian the potential energy is "energia potentială", that is the reason for "p" indexed.

#### Trailblazer

##### Moderator
Staff member
I do not know how to cancel a reply to a post, so I think this answer will appear above new diagram of the Trailblazer, that without the dotted circle (post #66).

In my understanding the sea level cannot be below the Gulf of Mexico floor and, as the Gulf of Mexico floor in included in r1, which is higher than r2 with more than six kilometers, the Mississippi cannot flow toward a sea level which is more than six thousand meters higher than its source.

I think that the green line is wrong drawed as there is no mountain between the Itasca lake and the Gulf of Mexico. Why did you say that I am missing the sea level?

Sea level is not "below the Gulf of Mexico floor". Why do you imagine that it is? The Gulf of Mexico floor is underneath the sea in the Gulf of Mexico, where it belongs.

And the green line is simply showing land sloping downhill from the source to the mouth. It is not meant to be an accurate representation of the Mississippi watershed, simply a diagram of land being higher above the sea at one end than the other.

Potential energy is Ep=mgh, where Ep is potential energy, m the mass of the object, g the acceleration of gravitation and h the altitude. We are not agreeing on h.

h is the height above a given reference level, to which you are relating the potential energy. If you are measuring the potential energy relative to sea level (which is what you do to see whether something is above or below sea level) then clearly h is the height above sea level, by definition.

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#### Z.W. Wolf

##### Senior Member.
Potential energy is Ep=mgh, where Ep is potential energy, m the mass of the object, g the acceleration of gravitation and h the altitude We are not agreeing on h.

I do not know how you are noting potential energy in english books, so I used my high school simbols. In romanian the potential energy is "energia potentială", that is the reason for "p" indexed.

The critical factor you are missing: You are not including the kinetic energy from the earth's rotation. Once again, you must factor in the centrifugal force

Let me try another way:

The equatorial bulge is caused by the earth's rotation. The earth's surface at the equator is farther away from the center of the earth than the surface of the earth at the poles. Why? Please answer before we go on.

#### Trailblazer

##### Moderator
Staff member
New diagram time. I've filled in the rest of the "Earth's surface". Again obviously the undulations are vastly exaggerated. Where the blue sea level ellipse is outside the green Earth surface you have sea. Where the green Earth surface is outside the blue sea level ellipse you have land sticking out above the sea.

Again, ignore the fact that the Mississippi appears to be rising from the highest peak on Earth - that's not relevant. The river could be flowing down any of those slopes towards the sea.

Any land outside the blue ellipse is above sea level, which is the zero point we measure height from.

(In reality the "sea level" isn't a perfect ellipse, because the varying shape and density of the Earth itself perturbs the gravity by a tiny amount as well, but that's not important right now!)

#### Clouds Givemethewillies

##### Senior Member
Potential energy is Ep=mgh, where Ep is potential energy, m the mass of the object, g the acceleration of gravitation and h the altitude. We are not agreeing on h.

I do not know how you are noting potential energy in english books, so I used my high school simbols. In romanian the potential energy is "energia potentială", that is the reason for "p" indexed.

You probably have a problem with 'frames of reference' for 'h'. ie. Relative to what?
For your formula to work it has to be relative to a plane that gives a constant value for PE for a constant value of h.

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#### Ion

##### New Member
New diagram time. I've filled in the rest of the "Earth's surface". Again obviously the undulations are vastly exaggerated. Where the blue sea level ellipse is outside the green Earth surface you have sea. Where the green Earth surface is outside the blue sea level ellipse you have land sticking out above the sea.

Again, ignore the fact that the Mississippi appears to be rising from the highest peak on Earth - that's not relevant. The river could be flowing down any of those slopes towards the sea.

Any land outside the blue ellipse is above sea level, which is the zero point we measure height from.

(In reality the "sea level" isn't a perfect ellipse, because the varying shape and density of the Earth itself perturbs the gravity by a tiny amount as well, but that's not important right now!)

I said that the green line is wrong not because it was too high but because it does not respect the WGS84 or any other geodetic system as the mouth of the Mississippi river has to be higher than its source because it is at a lower latitude. From the point of view of land above and below sea level is correct, but if I draw a line from where you wrote "Source" to the center of the Earth is longer than the line drawed from the mouth of Mississippi to the center of the Earth, which contradict WGS84.

Please, for an easier reference, put an "A" at the Mississippi mouth, an "B" at the source and an "O" at the center of the Earth! Or any other letters used in english books.

#### Z.W. Wolf

##### Senior Member.
I think it's time to stop.

#### Ion

##### New Member
The critical factor you are missing: You are not including the kinetic energy from the earth's rotation. Once again, you must factor in the centrifugal force

Let me try another way:

The equatorial bulge is caused by the earth's rotation. The earth's surface at the equator is farther away from the center of the earth than the surface of the earth at the poles. Why? Please answer before we go on.

Kinetic energy in romanian is "energia cinetică" Ec. For a body in motion that is Ec=[m(v squared)]/2, where m is the mass of the water volume which you wish to consider, v is its speed, all in SI units, I forgot to mention at the potential energy formula. That because I am not used with feet per second or yards per second. But this kinetic energy has to come from a force, which in case of a river is gravitation. Here I cannot apply gravitation as gravitation is toward the center of the Earth and I have to add it at the friction force. As you said, the Mississippi mouth is farther away from the center of the Earth, which means higher than its source.

In order to answer your "why?" I would say because the Earth rotation, as in a car in a curve, when you are pushed away from the center of the curve.

#### Trailblazer

##### Moderator
Staff member
From the point of view of land above and below sea level is correct, but if I draw a line from where you wrote "Source" to the center of the Earth is longer than the line drawed from the mouth of Mississippi to the center of the Earth, which contradict WGS84.
How does it contradict WGS84? The WGS84 system approximates the Earth's sea level to an ellipsoid with the longer axis at the equator, just as I have done with my blue circle, which represents a cross-section through the ellipsoid.

As you said, the Mississippi mouth is farther away from the center of the Earth, which means higher than its source.

Again, no it doesn't. You can be further away from the centre of the Earth, but still lower compared to sea level (or the WGS84 ellipsoid, which approximates it). That's exactly what my first diagram shows.

Let me label it up...

#### Ion

##### New Member
For Trailblazer: You wrote "You can be further away from the centre of the Earth, but still lower compared to sea level [...]" and that is true in certain points only. How came that the Mississippi mouth it is not higher than its source in WGS84? Why did you wrote "Again, no it doesn't"?

#### Ranon151

##### New Member
Think about it this way, sea level is not an arbitrary surface because by definition that's the point where the oceans of the world have already "evened out", so to speak. So your question should really be framed as "why aren't the waters in the equator all flowing northwards?"

Let's imagine an object slightly above the ocean in, say, the Tropic of Cancer. If the Earth was not spinning, the net forces on the object would be pointed straight towards the Earth's core. At our current sea levels, this force would point at a slight angle against the ocean surface. Due to the centrifugal forces of the Earth's rotation, however, the forces are slightly corrected, and point normal to the ocean's surface. This will be true at any point along the ocean's at sea level; by definition, the forces have settled so that the normal forces of the ocean surface have canceled out gravitational and centrifugal effects. Well, except for Coriolis effects, but that's not relevant here.

#### Trailblazer

##### Moderator
Staff member
How came that the Mississippi mouth it is not higher than its source in WGS84?
Because heights in WGS84 are defined relative to the WGS84 ellipsoid, which is the blue line on my diagram.

Labelled up this time:

Centre of Earth = O.

River flows from R1 to R2, where R1 is the source, and R2 is the mouth, which is at sea level.

OA = distance from centre to sea level at latitude of R1 (on this diagram, because of the vast scale exaggeration, it looks as if the mountain is at a "higher" latitude, but that's just an artefact of the diagram)
OR1 = distance from centre to river source.
OR2 = distance from centre to sea level at latitude of R2. (And therefore also to the river mouth)

AR1 = height of river source above sea level.
Height of river mouth above sea level = zero, by definition.

OA = OB.

OR1 = OC.

So clearly you can see that R1 is closer to the centre of the Earth than R2, by a distance CR2. But that doesn't stop it being higher than sea level, and therefore uphill from R2, which is at sea level. (AR1 is greater than zero)

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