Moshe Morris

[Moshe Morris @moshemo613]

I love the interplay of math and art.

But it's hard to see the art if we don't first understand the math.

So let's see if we can change that.
Let's take the time to break this equation down step by baby step until we understand it.

And then, when we are done, we can step back and appreciate its mathematical (and therefore artistic) beauty.

Part 1 coming soon...

[Abakcus @abakcus]

The Gaussian Integral is like pure art!

[Moshe Morris @moshemo613]

Who said the police are evil? Certainly not me.

But it's not an either or.

The police are necessary and deserve our support.
That doesn't mean we should turn a blind eye to obvious issues within the police department.

Illegally entering someones home without a search warrant and arresting them violates the very foundation of American law - and should be treated accordingly.

We can do that and at the same time push back against any and all attempts to portray legitimate and legal police action as something illegal or immoral.

It's not either/or.

[Moshe Morris @moshemo613]

A few points.

ONE: qualified immunity does not protect police officers from criminal prosecution.

Rather, it provides government officials with protection against personal liability in certain civil lawsuits, particularly when they have not violated a clearly established constitutional right.

---

TWO: Police officers are also not the only people who receive qualified immunity or comparable legal protections. A partial list includes:

• Law-enforcement officials
• Public-school and education officials
• Executive government officials
• Judges and prosecutors
• Legislators
• Witnesses

The precise protection, though, differs depending upon the person and the function being performed.

For example, witnesses may receive more immunity than police officers.

---

THREE: Why do these protections exist?

Because we do not want police officers hesitating during an emergency because they fear that a reasonable mistake could expose them to personal liability and years of litigation.

The same basic concern applies to other public officials.

We do not want principals afraid to discipline students, government officials afraid to make difficult decisions, judges afraid to rule, or witnesses afraid to testify because every disputed decision could produce a personal lawsuit.

---

IN SHORT

Police officers who abuse their authority are a real problem that must be addressed.

But protecting citizens from abuse and protecting officials who make reasonable, good-faith decisions are two separate concerns, and a responsible legal system must confront both.

[Moshe Morris @moshemo613]

It needs to be reformed and properly applied (not abused).

I do not want to go to the opposite extreme.
That just creates a new problem to solve an existing problem. That's not a good idea.

Either way, as far as I understand qualified immunity does not relate to the above video. The above video is about a wanton disregard for the law by the cops.

Qualified immunity is about protecting officers from reasonable mistakes made in the course of honestly trying to do their job.

That's not at all what happened here.

[Moshe Morris @moshemo613]

Or put it back into a healthy balance.

Qualified immunity has a legitimate purpose.
If a cop makes a reasonable mistake, he needs to be protected.

We can't ask people to go out and take on difficult and dangerous jobs and let them be financially ruined if they make a reasonable mistake when doing so.

But the above video (and countless other examples) are not examples of reasonable mistakes.

They are examples of willful ignorance and/or disregard for the law. And they should be treated as such.

And, as you noted, this often times goes deeper than the individual cop. It can be the entire department — as well as the local prosecutors also.

Not sure how to deal with all of those problems.
But I do think that a good place to stop is to hold cops (and others) criminally responsible if the evidence shows will neglect or disregard for the law.

[Moshe Morris @moshemo613]

There are laws on how you can and cannot arrest someone.

The constitution is the LAW OF THE LAND!
Violating the constitution is violating the law.

It is not patience to ILLEGALLY put your foot in someone's door and ILLEGALLY demand that they step outside.

IF they wish, they can go to a judge and get a LAWFUL warrant for his arrest (although I'm not sure they can get one).

But that would require REAL PATIENCE. The patience to actually follow the law and go through the procedures set out by the law.

[Moshe Morris @moshemo613]

The answer is b --> 2^99

NOTE:

2² = 4
2³ = 8
AND: 8 - 4 = 4
OR 2³ - 2² = 2²

NOTE AGAIN:
2³ = 8
2⁴ = 16
AND: 16 - 8 = 8
OR: 2⁴ - 2³ = 2³

We can keep this going:

2⁵ - 2⁴ = 2⁴
2⁶ - 2⁵ = 2⁵
2⁷ - 2⁶ = 2⁶
2⁸ - 2⁷ = 2⁷

And so on.

So now, let's take a look at our problem:
2^100 - 2^99

What does that equal?
It's the same pattern.

So the answer is b --> 2^99

[Moshe Morris @moshemo613]

c + a + b = 300

NOTE
a + a = 2a
c + c + c = 3c
b + c + b = 2b + c

SO:

2a = 300
3c = 150
2b + c = 250

NOW, let's simplify the first two equations.
2a = 300 --> a = 150 [divided both sides by 2]
3c = 150 --> c = 50 [divided both sides by 3]

Here is what we have so far:

a = 150
c = 50

Now, let's take a look at our third equation

2b + c = 250

We cannot simplify it.
WHY?
BECAUSE: we have only one c.

But, that one c is helpful.
WHY?
BECAUSE: we know that c = 50
SO: Let's rewrite it

2b + c = 250 --> 2b + 50 = 250

Rewrite again: --> 2b = 200
And simplify: b = 100

now we have a, b and c each by themselves:

a = 150
b = 100
c = 50

Now, remember what we are solving for:

a + b + c

That's easy now
150 + 100 + 50
Which equals 300

And that is the answer:

a + b + c = 300

[Moshe Morris @moshemo613]

The parrot is 30 cm tall.

---

Let's turn this into an algebra equation.

we will have m be short for man.
and p will be short for parrot.

Now let's create our starting equations:

m + p = 220
m - p = 160

now -- let us subtract the two equations from each other (yes, you can add or subtract equations).

(m + p = 220)
- (m - p = 160)

I used the parenthesis just to clarify that I'm subtracting one equation from the other.

So how do we do this?
Well, the right hand side is easy.
220 - 160 = 60

But what about the right hand side?
That's also straight forward.

I subtract (m + p) from (m - p).

(m + p)
- (m - p)

That equals:

m - m
+
p - (-p)

And that equals 0 + 2p

Put it all together --> 2p = 60

Which means that p = 30.
I.e, the height of a parrot is 30 cm.

And that's my answer --> the parrot is 30 cm tall.

---

Think of it this way — subtraction is about difference.
What is the difference in the height of the man plus the height of the parrot from the height of the man minus the height of the parrot?

Well, let's note --> the height of the man stays the same. The only thing that changes is whether we add the height of the parrot -- or subtract it.

So the difference is the equivalent of two parrots.
And that is the difference between 220 and 160.

OR: the height of two parrots equals 60.
SO: the height of one parrot equals 30.

[Moshe Morris @moshemo613]

Formally speaking — a side in geometry is a straight line segment which joins two adjacent vertices.

SO: a square has four sides.
BECAUSE
a) there are four straight lines
b) each straight line connects a vertex on each side.

NOW:
since a circle has no straight lines
and no vertices
therefore it technically has no sides.

Informally speaking — people do talk about a circle as having only one side.

so...

IF we are speaking formally --> there are no sides.
IF we are speaking informally --> then there is one side.

[Moshe Morris @moshemo613]

One cockroach weighs 9 kg.

Let's make this a proper algebra problem.

c is for cats.
r is for rats.
k is for cockroaches [sorry, c is already taken]

SO: 3c = 36 kg
SO: c = 12 kg

ALSO: 2c + r = 34 kg
AND: c = 12 kg
SO: 24 kg + r = 34 kg
SO: r = 10 kg

NOW: r + 2k = 28 kg
AND: r = 10 kg
SO: 10 kg + 2k = 28kg
SO: 2k = 18 kg
SO: k = 9kg

ALL TOGETHER NOW

c = 12 kg
r = 10 kg
k = 9 kg

LET'S VERIFY

3c = 12 kg * 3 = 36 kg --> check
2c + r = 24 kg + 10 kg = 34 kg --> check
r + 2k = 10 kg + 18 kg = 28 kg --> check

THEREFORE --> one cockroach weighs 9 kg.

And that is our answer.

[Moshe Morris @moshemo613]

Body cams go both ways.

They can help show when the cops are in the right.
But they can also help show when the cops are in the wrong.

The police have become too much of a political divide.
Either we support them or revile them.

Policing is obviously a hard job.
And there are many dangerous people out there.
And cops do at times put their lives on the line to help protect everyone else.

As such, they deserve our support.

At the same time, police have a legal license to violence that the rest of society simply does not have.

And it is also obvious that there are cops who abuse that license.

Either willfully.
Or through negligence.
Or lack of proper training.

In such cases, they need to be either tried in a court of law, disciplined and/or be given better training.

Either way, body cams are essential devices in so many ways. They provide crucial information as opposed to simple claims from one side or the other.

Remember, cops can also lie (and have lied).
Same is true for the accused.

But they can also tell the truth (and have told the truth).
Same is true for the accused.

The video footage from body cams helps us determine who is telling the truth and who is not.

Who is being lawful and who is not.
Who is being violent and who is not.

As such, having one body cam per vehicle stop is a step in the right direction.

But it's just a step.
All federal law enforcement agents should be required to use body cams unless there is some substantive reason why doing so would either endanger them or impede them in doing their service.

[Moshe Morris @moshemo613]

In geometry, the diagram has a particular purpose — and it is not to be accurate in terms of measurements and scale.

Rather, its purpose is to show the configuration of the geometric problem.

For example:

Which lines intersect.
Which angles are adjacent.
Which shapes share sides.

These relationships can be difficult to describe verbally.
It is much easier to display them graphically.

And these structural relationships do need to be accurate.

However, there is no requirement that the diagram visually reproduce the stated lengths, angles, or proportions accurately or to scale.

For example:

IF a diagram indicates that all three sides of a triangle are equal with tick marks

THEN they are mathematically equal — even if in the diagram it is clear that one side is longer than the other.

That last fact — that the diagram indicates that one is longer than the other — has zero bearing on the problem. The ticks indicate the mathematical facts.

And a bad diagram does not change that.

In terms of the mathematical problem, they are equal. And to treat them otherwise is to ignore the mathematical problem in front of us.

The same is true in our case.
50° is 50° is 50°.

It matters not whether or not the diagram is in sync with that fact or not.

That's the data given.
That's the problem to be solved.

If one thinks there is a mistake — then they should inquire of the person making the problem.

IF they say yes
THEN you can change the problem.

Until then, though, the problem is as the problem is written.

In short, the diagram conveys the structure.
The markings and labels determine the measurements.

And confusing the two is a mistake in interpreting the problem.

One simply cannot conclude or argue that the measurements change because the diagram is not visually in line with the measurements — unless the problem itself explicitly tells you that the diagram is written to scale.

But barring such information, the facts are the facts. And arguing from the diagram is simply not a mathematical argument.

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P.S. Why am I spending so much time discussing this? To help flesh out the issue and to clarify some of the points I am making above.

Take care :-)

[Moshe Morris @moshemo613]

I'm just telling how I understand a math problem like the one in front of us works.

We are not measuring anything.
We are solving a geometry problem.

And that means relating to the information given.
And how the diagram looks cannot override that.

Again, as far as I understand, that's just the "rules" of math.

[Moshe Morris @moshemo613]

On that we will have to disagree.

It is 50°.
Clearly labelled.

If there is a disagreement between the diagram and the information provided, we go with the information provided. Not with the diagram

If we have to assume that there was an error, our assumption should be that the diagram was not drawn carefully or exactly.

Unless we are told that the diagram was drawn to scale.

Since we were not told otherwise, the angle is 50° and not 60°.

[Moshe Morris @moshemo613]

Because the accuracy of the diagram is immaterial to the mathematical problem unless stated otherwise.

And it was not stated otherwise.

And the problem is 100% coherent with 50°.

Either way, mathematically speaking it doesn't matter.
IF the angle is 50° THEN the answer is 10°.
IF the angle is 60° THEN the answer is 20°.

The essential math problem is the same either way.

[Moshe Morris @moshemo613]

The problem is that this is a geometry problem, not a measurement exercise.

As such, we determine the geometric relationships from the information given unless the diagram explicitly states that it is drawn to scale.

But that is not the case here.

The 50° angle is explicitly given.
The triangle is explicitly marked as equilateral.
The lines are not marked as parallel.

Therefore, their apparent visual alignment cannot override the actual mathematical information provided.

[Moshe Morris @moshemo613]

If it is parallel, you would be correct.

But there are no indications in the problem and/or diagram that they are parallel.

True, they make look parallel to the naked eye.
But that contradicts the information given.

And given that the information given is a coherent math problem, I don't think we should change it just because the lines look parallel.

[Moshe Morris @moshemo613]

The answer is 24m²

The shaded triangle is a right triangle
[do you see why? If not, let me know.]

It has a height of 8
We know that from the square
[again, do you see why?]

And it has a hypotenuse of 10

So we can apply the Pythagorean theorem

8² + b² = 10²
OR: 64 + b² = 100
OR: b² = 100 - 64
OR: b² = 36
SO: B = 6

Now we can figure out the area.

Width: 6
Height: 8

Area: (6 * 8) / 2
OR: 48 / 2
OR: 24

And that is our answer --> 24m²