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Programs > Service-Learning
Project Ideas

The links below will take you to a page with project ideas specifically for that category. Many projects address more than one issue as a product of their scope and breadth; when this happens, a project may be listed in more than one category. The overwhelming majority of these projects address a variety of subject matters and indicators from the Maryland State Curriculum, and these projects can be altered to include other areas of study as well.

Within the pages, the projects have been sorted by their level of service – direct, indirect, and advocacy.

Within the levels of service, the projects have been listed alphabetically by project title.

Recommendation: Because some of these pages will have dozens of project descriptions, it may help you to use the “Find” feature. On some browsers, hitting Ctrl+F will open a toolbar or pop up box that will allow you to search the whole document or web page for a specific keyword or phrase.

          In this category, you will find projects aimed at assisting senior citizens. Many of these projects involve visiting nursing homes in conjunction with learning about history or caring for the elderly. Some schools have adapted projects so that they are working with a local senior citizen center to get the senior citizens to their school for events such as a senior citizen prom. If you are looking for project specifically involving veterans, see Public Safety.

          In this category, you will find projects aimed at preventing animal cruelty and promoting animal safety. Projects may include visits to local animal shelters to assist and promote safe practices for animals. For projects about indigenous species and the environment’s impact on animals, see Environment.

          See School Improvement.

Civic Engagement

          The goal of these projects is to increase public awareness, support, and engagement for our democratic society. Many of these projects will be aimed at increasing the number of voters and mobilizing groups of citizens to change their community for the better. Other projects in this category prepare students to become leaders for a variety of service-learning activities.

Cultural Diversity

See Education.

Disability Awareness/ Support

          For disability awareness and support within the schools, see School Improvement.

          For disability awareness and support in the community, see Health.

These projects are aimed at promoting literacy, preserving the past, and affecting the future. Many of these projects include student tutoring or mentoring services and sister schools. Other projects involve continuing education and may fundraise to provide scholarships for students attending college. For projects specifically aimed at preserving the memories of veterans, please see Public Safety.

          These projects are all about affecting the environment in a positive way. Many of these projects will include the restoration of indigenous species, the clean up of local landmarks, and promoting more environmentally friendly practices in the school and local community.

          This category includes promoting healthy living styles as well as providing assistance to those who are ill. These projects can range from helping special education students learn about hygiene to writing letters for donations to businesses to aid a local charity that helps kids with chronic illnesses.

          The projects in this category are meant to target helping those who are homeless and impoverished. Many of these projects also tackle world hunger or benefit local soup kitchens.

          For addressing prejudice in schools, see

-      School Improvement, Bullying Prevention/ Peer Mediation

-      School Improvement, Cultural Diversity

For addressing prejudice in the community, see Public Safety, Promoting Peace

Public Safety

          The projects in this category are aimed at promoting public safety through law enforcement, preparing for and recovering from disasters, supporting the military and veterans, supporting victims of abuse, and promoting peace in the local and global community. These projects can include anything from beautifying community spaces to interviewing veterans so their military experiences are not lost.

School Improvement

          This includes school beautification, character education, disability awareness in the school, and anti-bullying campaigns. These projects are designed to directly impact school safety and morale. Bullying has become a targeted problem in schools across the country. The projects found here will be focused on bullying prevention in schools and online.

Substance Abuse

For projects aimed at substance abuse prevention and helping the victims of substance abuse, see Public Safety.

Levels of Service

Direct Service: Students have face-to-face contact with the service recipients. For example: tutoring; serving meals at a homeless shelter; working with the elderly in a nursing home, etc.

Indirect Service: Students perform a service without having face-to-face contact with the recipient. Usually resources are channeled to help alleviate a problem. For example: food & clothing drives; walk-a-thons or fundraisers; environmental projects, etc.

Advocacy: Students educate others about a particular issue with the goal being to eliminate the cause of a particular problem. For example: writing letters to legislators or editors; preparing and displaying posters, plays, or other educational materials for others, etc.

Contact Information
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Email:  jayers@msde.state.md.us
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Social Media

Gowalla Turns the Tables, Integrates With Foursquare

Gowalla, the popular geosocial network, has released version 3 of its iPhone app, an update that not only includes an improved interface and new features, but deeply integrates the app with Foursquare, its bigger and better-known rival.

Gowalla 3 is focused on reducing the barriers to checking in, improving the visuals of the interface, and adding new tools to make checking in more fun and useful. It makes its debut in the iPhone app store today and on other mobile devices in early 2011, starting with the Android.

It is the company's decision to integrate Gowalla with Foursquare, its rival in geolocation, that will capture all of the headlines, though. The Foursquare integration has two key components. First, Gowalla now lets you broadcast your checkins on not only its app, but Twitter, Tumblr, Facebook Places and Foursquare as well. Gowalla even lets you earn Foursquare badges and Facebook Deals through the iPhone app. As an added bonus, Gowalla also pulls in Foursquare Tips whenever you check in.

The second component of the Foursquare integration is just as impressive, though. Gowalla has created a new Universal Activity Feed, an aggregated stream of checkins coming from Foursquare, Gowalla and Facebook Places. Instead of opening up multiple apps to see where your friends are hanging out, you can see all of their geosocial activity from one interface.

Gowalla 3 has other new features, as well. It has added better Retina Display support, moved the check-in button into a more prominent location, added photos to the Activity Feed, and bookmarking for keeping track of your favorite locations. There is also a new feature called Notes that lets you leave short messages for your friends as specific locations the next time they check in. Unlike Foursquare Tips, each Gowalla Note is only meant for one person, which makes leaving a cute note for your boyfriend or girlfriend at your favorite spot a far more intimate experience.

What Will Foursquare Do?

Gowalla CEO Josh Williams explained to Mashable that the company's future is as a "socially curated guidebook." It's not focusing on delivering deals (there are many ways to get deals, from coupons to group buying) or providing elaborate game mechanics. Instead, it wants to help users discover locations through useful information delivered in a fun way. The geolocation startup is trying to solve the problem of how to get a smile on a person's face every time they check in. It even wants to making checking in to the same location (say a coffee shop) a unique experience each time.

The new Gowalla isn't a radical reinvention of the service; it still has checkins, an elegant design and the same Trips and Stamps that have helped it cultivate an active userbase. However, its decision to add Foursquare positions Gowalla as the richest universal check-in app on the market.

Gowalla did not work with Foursquare on this integration; it was all done through the API. That leaves the real possibility that Foursquare could throw a big wrench into Gowalla's plans by blocking its rival's use of the API. The threat posed by Gowalla 3 is real; that alone could force Foursquare's hand in the name of competition. It would also create a firestorm of controversy.

The ball is now in Foursquare's court. Will it let Gowalla use its API, despite the potential damage it could cause its business? Will it block Gowalla, potentially igniting a developer and anti-competitive controversy? Could it even turn the tables by adding Gowalla integration into its app?

Gowalla has thrown down the gauntlet. It's Foursquare's move now.

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Make Tea Time Terrifying With These Creature Cups

Cream and sugar can only do so much. If you really want to liven up your next cup of coffee, beyond the traditional boundaries of lactose and artificial sweeteners, consider one of these mugs.

They're called Creature Cups, and they're exactly what you'd hope they would be. Each mug is specially designed with a creepy surprise dwelling at the bottom: skulls, tarantulas, alligators and lobsters — the whole gang's there.

Fill one to the brim, hand it to a friend and wait for the scream. Just be sure you're standing outside the spit zone.

For less scary surprises, there's also a similar line of mugs with adorable animal molds hiding below the surface — less "ahh!" and more "aww."

Check out the full Creature Cups set here. Sound like something you'd use? Tell us what you think about it below.

Image courtesy of Flickr, stefg74

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36 Songs to Celebrate the 2014 Rock and Roll Hall of Fame Inductees

The Rock and Roll Hall of Fame announced on Tuesday it has whittled down the original list of 16 nominees to six artists that will be inducted in 2014.

Grunge pioneers Nirvana made it into the hall on the band's first try after becoming the youngest act ever to be nominated for entry. 1980s pop duo Hall and Oates and tongue-wagging rockers KISS were also selected for entry, with solo artists Peter Gabriel, Cat Stevens and Linda Ronstadt completing next year's shortlist.

In Mashable's Hall of Fame poll from October, Nirvana registered more than 25% of the 2,511 votes from our readers, followed by by KISS with 12%.

In honor of the six acts being welcomed into the Rock and Roll Hall of Fame, we rounded up some of their best hits of all time into a Spotify playlist, which you can stream below. If you have a favorite track from one of these artists that you don't see here, let us know in the comments. We'd also love to hear who you think should be inducted next year.

Have something to add to this story? Share it in the comments.

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Cie Games

Social Gaming Will Generate $1 Billion This Year [STATS]

Social gaming is poised to become a billion-dollar industry this year, according to new research from eMarketer. Approximately 62 million U.S. Internet users -- that's 27% of the total Internet-using population in the U.S. -- will play at least one g...

Honda Takes Social Gaming for a Test Drive

It's not unusual for a large car company like Honda to advertise its newest release on a billboard -- unless, of course, that billboard exists in a virtual gaming community on Facebook. To promote the U.S. launch of its latest sport hybrid coupe, the...


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Are there any ways to visualize(plot/draw) points on a high dimensional (ex: dimension = 5) manifold?

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Heh, there's a joke about that. An engineer goes with a mathematician friend to a geometry seminar. Afterwards, the mathematician asks him what he thinks. "Well, when he gave the examples in one and two dimensions, I followed it. But how do you guys picture high dimensional manifolds, say 5?" "Simple, start by picturing an $N$-dimensional manifold, then set $N= 5$." –  Willie Wong Jan 25 '11 at 12:08
Exactly the same ways with which you can visualize 2- and 3-manifolds: considering projections, level sets for various functions, etc. –  Mariano Suárez-Alvarez Jan 25 '11 at 12:22

2 Answers 2

up vote 9 down vote accepted

A usual way to work is to take slices, CAT-scan style.

Have you seen a CAT-scan? It represents a 3-dimensional object as sequence of two-dimensional slices of the object, in a way that you can choose which directions your slices cut (after computer processing).

There are two usual ways of representing a 3-dimensional object on a plane. You can take projections (think a picture of the "outside" of the object) or slices. Similarly, to represent higher ($N$) dimensional objects on a plane (draw it on a piece of paper), you must throw away $N-2$ degrees of freedom. Each degree of freedom you can choose to throw away by projection or by slicing. So a typical way of visualizing a 4-dimensional object is to take a sequence of 3-dimensional slices, and project each slice onto a computer screen, and display this sequence one-by-one over time. This way you get the illusion of a 4 dimensional object "passing through" our three dimensional world.

Higher dimensional objects can be done similarly, you just need to take more slices.

One fun thing you can do with this is to try to play 4-dimensional tic-tac-toe. To make the game not a trivial win for the first player, you need a $5\times 5\times 5 \times 5$ grid, and first to make 5 in a row wins. So on paper you need to draw a $5\times 5$ matrix of $5\times 5$ grids, each grid represent the intersection of two orthogonal hyper-slices of the full 4-dimensional game grid.

Another fun way to develop some intuition on higher dimension spaces is to spend some time playing Magic Cube 4D, a higher dimensional analogue of Rubik's cube. (It could also get you dizzy pretty quickly).

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4D object passing through.. ie time! –  bobobobo May 20 '12 at 22:47

Well, here's how I think about it.

Every time you add a dimension, you need an infinite number of the previous dimension.

1D is the x-axis. You need a line to visualize.

1D -> 2D means you need an infinite number of additional x-axes (call them y-axes). You need a plane to visualize (flatland picture).

2D -> 3D means you need an infinite number of additional xy planes. You need a space to visualize (3d picture).

3D -> 4D means you need an infinite number of additional xyz spaces. You need a movie to visualize.

4D -> 5D means you need infinitely many vhs cassettes, each with a movie on it to visualize.

So buy some VHS! They are cheap now.

(really, like Willie Wong said, to take a "slice" of the 5d space, by fixing one of the variables. Then, you can create a "movie" of the other 4 variables (use 3 for space, and 1 for time). to visualize the whole space though, you would need an infinite number of these "movies" (and would each be infinite in duration), for each value you want to the 5th variable to).

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These questions are motivated only by curiosity.

Take a Young tableau of shape $(\lambda_1,\lambda_2,\ldots,\lambda_n)$, where $\lambda_1\geq\lambda_2\geq\ldots\geq \lambda_n)$. Is there any physical meaning or importance to the eigenvalues of such a tableau when embedded into a matrix (putting zeros outside the shape)? To be clear, I'm interested in combinatorial meanings. For example,

\begin{pmatrix} 1 & 2 & 5 & 6 \\ 3 & 4 & 8 & 0 \\ 7 & 10 & 0 & 0 \\ 9 & 0 & 0 & 0 \end{pmatrix}

has eigenvalues $\{-9.73,-5.43,5.62,14.53\}$.

Alternatively, instead of writing in the young tableau square values, write in the hook lengths of each square: \begin{pmatrix} 7 & 5 & 3 & 1 \\ 5 & 3 & 1 & 0 \\ 3 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{pmatrix}

The product of the hook lengths is intimately connected to the number of young tableaux of that shape. Is there a meaning to the eigenvalues of the resulting matrix? Obviously the determinant will be just 1 in this case, and 0 for anything non-staircase.

Hypothetically, the hook-length matrix (as well as the square value matrix) can be interpreted as an adjacency graph, so I can see the eigenvalues corresponding to something akin to the spectrum of the corresponding graph.

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If I had to guess I'd say pretty confidently that the matrix formed out of a tableau carries no special information about it. Also, tableaux is already the plural of tableau - no extra s needed. –  anon Dec 20 '12 at 4:39
You should expect the eigenvalues of a matrix to be meaningful if it is meaningful to think of that matrix as a linear operator acting on a single vector space. For example, the eigenvalues of an adjacency matrix are meaningful because the adjacency matrix naturally acts on the vector space spanned by the vertices of a graph. I do not see a corresponding interpretation for Young tableaux (although I could of course be mistaken), mostly because there is no natural reason to force the corresponding matrices to be square rather than rectangular. –  Qiaochu Yuan Dec 20 '12 at 5:26

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I have rewritten this entire question, since what I've learned since asking it requires me to restate it. I want to get rid of the obfuscating revisions.

Let's say that f is a continuous function.

$f(x)$ approaches L as x approaches a. So $\lim\limits_{x \to a}f(x) = L$

When it's said that the gradient of a tangent line to a curve at some particular point has some particular value, this is the same as saying f(a)=L. But without explicitly evaluating at that point, you can't say as much. All you can say is what happens as you approach that value. In other words, you can only say what value $f(x)$ approaches as $x$ approaches $a$, you can't say what $f(a)$ is.

Is that true?

Some textbooks will just say that the value of $f(a)=L$. Sal Khan's explanation does this. He says, about the function as it approaches the limit, "this is the gradient of the tangent." I'm saying that it should be said that, "the derivative approaches the gradient of the tangent to the curve." I think "approaches" and "is" are very different.

If there is a way to prove that the $f(a)=L$ then I'd like to see it. I don't know how to do this yet.

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Since "=" is "equals", it says the limit is L. Exactly L. (By the way, one cannot assume that $f(x)$ is continuous, because $f(x)$ is a number and a number is neither continuous nor discontinuous. One could assume that the function $f$ is continuous.) –  Did Jan 4 '12 at 18:23
@Didier: the part of your remark about "$f(x)$" is technically correct but on the pedantic side. At least in the United States, speaking of "the function $f(x)$" is widespread practice among textbooks and instructors as well as students. We shouldn't say it, but we often do, and it doesn't (necessarily!) mean that we don't know the difference between a number and a function. –  Pete L. Clark Jan 4 '12 at 18:25
@Didier, I actually appreciate your pedantry, I hadn't thought of it like that before. Now that you say it, it seems obvious. I will edit to clarify. My questions still stands, however. –  Korgan Rivera Jan 4 '12 at 18:32
The phrase "$\lim_{x\to a} f(x)$ approaches $L$" conveys absolutely the wrong impression. A mathematician would never use it. One can say, correctly albeit informally, that $f(x)$ approaches $L$ as $x$ approaches $a$. The limit is (in this case), just a plain number, not at all a forever dynamic or moving process. Think of "She has arrived in Winnipeg." Winnipeg is a fixed place, the fact that she travelled to get there does not change that. –  André Nicolas Jan 4 '12 at 19:12
Is the curve you're considering the graph $y=f(x)$? If so then the gradient of the tangent to the curve at $a$ would be $f'(a)$, not $f(a)$. –  Adina G Jan 4 '12 at 21:23

3 Answers 3

up vote 5 down vote accepted

The confusion seems to be in your line

$\lim\limits_{x\to a}{f(x)}$ approaches $L$.

It is $f(x)$ that approaches $L$.

That is, the function $f(x)$ approaches some value as $x$ tends to $a$. That value is called the limit, and is denoted $\lim\limits_{x\to a}{f(x)}$. Saying $\lim\limits_{x\to a}{f(x)}=L$ is saying these two values are equal.

The derivative $\frac{dy}{dx}$ is the gradient of the tangent line, which is the limit of gradients of successively smaller secants. Again, a limit is a value, not something that approaches a value.

Edit: let me see whether I can help with your rewritten question.

Suppose $f$ is a continuous function. Then $\lim\limits_{x\to a}f(x) = f(a)$ (this is by definition of continuity -- we haven't taken derivatives yet).

Now suppose $f$ is differentiable at $a$, and suppose $f'(a) = L$ -- that is, $$\lim\limits_{h \to 0} \frac{f(a+h)-f(a)}{h} = L$$.

The function $$g(h) = \frac{f(a+h)-f(a)}{h}$$, which is defined for $h$ non-zero, represents the gradients of secants. The function $g$ approaches $L$ as $h$ tends to $0$ -- this is what it means for $f$ to be differentiable at $a$. So $g$ approaches the gradient of the tangent to the curve at $a$. But $g$ is not the derivative. The derivative is $\lim\limits_{h\to 0}g(h)$, which is $L$.

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So what I should have said was $f(x)$ approaches $L$ as $x$ approaches $a$. So $\lim\limits_{x\to a}{f(x)}=L$ Some texts then go on to say, however, that $f(a)=L$. Isn't that the assumption being made when saying that the gradient of a tangent line where $x=a$ is $L$? –  Korgan Rivera Jan 4 '12 at 20:06
@Korgan, it is not correct to say that $f(a)=L$ because $L=\lim_{x\to a}f(x)$. For any particular $f$ and $a$ it may of course happen to be true anyway. Or may not. –  Henning Makholm Jan 4 '12 at 20:12
I see my mistake now. Thanks. –  Korgan Rivera Jan 5 '12 at 1:54

This is the mere definition.

Letting $x$ approach $a$ then your function $f$ approaches some value $L$. You want to give this value a name. And you call it the limit of $f$ as $x$ goes to $a$, written $\lim_{x \to a} f(x)$.

Of course now $f$ approaches $\lim_{x \to a} f(x)$.

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When $x_n$ approaches some value $x$ as $n$ goes to infinity, then we say that the limit of $x_n$ is that value $x$. The limit is a number. A sequence approaches its limit (if it has one).

So you can't say "I understand that $\lim\limits_{x \to a}f(x)$ approaches $L$", since the limi $\lim\limits_{x \to a}[f(x)]$ is a number*, and the thing inside $\lim[\cdot]$ - in that case $f(x)$ - approaches $L$.

Coming to your question about existence of a limit.

(example 1) If the function $g:X\to Y$ is continuous and $a \in X$, then the limit $\lim_{x\to a}g(x)$ exists and is equal to $g(a)$. So: "when $x$ approaches $a$ then $g(x)$ approaches $g(a)$".

However it is possible that a function $h$ is not continuous at $a$, but still $\lim_{x\to a}h(x)$ exists.

(example 2) You can think about $h:X\setminus \{a\} \to Y$ such that $h(x)=g(x)$ from the previous example. If $a$ is not in the domain, we can't say about continuity there, but the limit obviously still exists.

(example 3) You can imagine $j(x)=\frac{x^2}{x^2+1}$ which has limits at infinity, so when $x$ approaches infinity, then j(x) approaches the limit, which is equal to $1$. There is no continuity here unless you know how to add infinities to your domain and define continuity for the enlarged domain.

(example 4) You can define a function $k$ equal to zero everywhere except for 0 where it is equal to one. It is artificial, but since in the typical definition of $\lim_{x\to a}$, one assumes that $x$ approaching $a$ is never precisely equal to $a$, then our function has limit at $0$ $\lim_{x\to 0}k(x)=\lim_{x\to 0}0=0$ but it (I mean the limit) is not equal to $k(0)=1$.

There is no such thing as "value at the limit". We just say that, since it is very handy. It is handy, because if the function is not defined in the limit point $a$, we may want to define it there, so then we add/define "value at the limit" to our function using its limit at this point.

(example 5) To produce $g$ (example 1) out of $h$ (example 2) we put $g(x) = h(x)$ for $x$ belonging to the domain of $h$ and $g(a) = \lim_{x\to a} h(x)$

*in the same way as $f(x)$ is a value, not a function

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Is it possible to have the cell brackets on the left? I looked through the options and couldn't find anything, but maybe it's some kind of esoteric style setting or something.

The reason I'm looking for this is because the content of notebooks is on the left, which means that's where my mouse hangs out most of the time. So I suspect having the cell brackets on the left would be more natural.

(I'm aware of the cellgroup openers, my question is about general selecting/manipulating, not just opening/closing).

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I don't know the answer, but one strong indication that it might not be supported is that cell brackets grow with nesting depth whereas the left margin (for L->R languages) is supposed to have a fixed indent (for a given type of cell). In other words, if you have several sections/subsections/subsubsections etc., the cell brackets would be 6-7 layers deep, which would indent your input further and further to the right, leading to some unpleasant UI feel and experience. I wouldn't be surprised if the answer was "no", but I could be wrong. –  The Toad May 20 '13 at 5:56
The answer is, indeed, no. –  John Fultz May 20 '13 at 12:29

1 Answer 1

up vote 6 down vote accepted

The answer is, indeed, no. – John Fultz

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damn. i was hoping to leave this one hanging open-endedly silent on the shoulders of WRI, so that it would nag and scrape at their subconsciousnesses until there was no recourse but to implement this feature. but alas @Rojo you've forced my hand. –  amr May 22 '13 at 18:43

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Topic: where's the center?
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where's the center?
Posted: Jun 20, 2013 10:22 PM
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An expanding balloon is the standard picture/analogy
to elucidate the expanding universe. OK, let's go
with that; an analogy ostensibly represents an ANALOG
to the subject, right?

The balloon is a 2-D surface, but in 3-D space,
there's a center. Inhabitants of Balloon World
are stuck within that surface. They cannot point
toward the center, but we can see it.

Now, extend to our universe, expanding space, yadada.
By analogy - remember that one? - there must be a
point in some 4-D space, surrounding us, which
constitutes the center. So, the question is, can
we 'point' to it, through some 4-D mathematical
abstraction, derived from our measurements?

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Teaching mathematics

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From: Cynthia (for Teacher2Teacher Service)
Date: Feb 18, 2006 at 08:54:52
Subject: Re: Teaching mathematics

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>To mathematics teachers: What is the main problem that you have
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You don't need a metric to define the differential of a function, and the cotangent bundle carries a canonical one-form.

But you do need a metric to define the gradient, and the tangent bundle does not have a canonical vector field.

These are not difficult truths, but still... why the preference toward "co"?

share|improve this question
I think the question, as written, is somewhat misleading. The tangent and cotangent bundles are equally canonical. They come for free with the differentiable structure. Another thing which comes for free with the differentiable structure are the smooth functions, which are arrows from the objects. Hence it is not surprising that contravariant functors are preferred. –  José Figueroa-O'Farrill Mar 6 '10 at 23:15
If you construct them as the tangent and cotangent sheaf, the tangent sheaf is easier to construct as it is nothing more than the sheaf defined by $T(U):=Der_{\mathbb{R}}(\mathcal{O}_{\mathcal{M}}(U),\mathcal{O}_{\mathcal{M}}(U))$. The cotangent sheaf is just constructed by the universal property of the module of differentials. –  Harry Gindi Mar 7 '10 at 0:03
In fpqc's formula the ring O_M(U) must be replaced with the restriction sheaf (O_M)|_U, just like definition of Hom sheaf. Otherwise it doesn't even make sense as a presheaf. As for the cotangent sheaf, a definition is no harder: (Delta_M)*(I/I^2) on M akin to algebraic case. Strictly speaking, modules of differentials in the algebraic sense are not logically relevant at this step since M x M is not built via tensor products (but the theories behave similarly, and for completed stalk calculations for analytic M the link with modules of continuous differentials is very useful) –  BCnrd Mar 7 '10 at 14:46
Ah, thanks for the correction. –  Harry Gindi Mar 7 '10 at 16:19
The word "canonical" seems to be an unintended pun (cf canonical transformations in symplectic geometry and all that). –  Victor Protsak Jul 17 '10 at 20:20

9 Answers 9

up vote 29 down vote accepted

If you want to differentiate functions from a manifold to (say) the real line R, then you want to use the cotangent bundle on the manifold.

If instead you want to to differentiate functions to the manifold from the real line (i.e. parameterised curves), then you want to use the tangent bundle on the manifold.

So the preference comes from whether you want to use the manifold as the domain or as the range of the functions one is differentiating.

share|improve this answer
Situation is opposite: If I want to differentiate a function on manifold at a point, then I need a tangent vector at that point. –  Petya Mar 7 '10 at 4:13
No, Terry's answer is right (see also the first paragraph of Deane's answer). A derivative is a linear approximation, so the derivative of a function $\mathbb{R}^n \to \mathbb{R}$ is a linear form on $\mathbb{R}^n$. In the case of a manifold this means you get an element of $T^*M$, which of course turns out to be the differential. –  Matt Noonan Mar 7 '10 at 4:51
This nicely captures the duality between the two, but are these answers really honest? Do y'all really think of these two structures with the democracy professed in these answers? I don't (I understand them, but I don't) and I have to twist my mind a bit to find the structure dual to the canonical form. Maybe it's just me. (Sorry, this isn't really a mathematics question.) –  Eric Zaslow Mar 7 '10 at 4:52
Democracy? Not really. In my answer, I definitely view the tangent bundle as being more fundamental, and the cotangent bundle as arising naturally from differentiating functions. On the other hand, the canonical 1-form and its covariant derivative make the cotangent bundle in many ways much more interesting to study for its own sake than the tangent bundle. –  Deane Yang Mar 7 '10 at 5:06
@Deane Yang: I suppose you mean "exterior differential" instead of covariant derivative! –  Orbicular Mar 7 '10 at 9:07

Neither is more canonical than the other. The tangent bundle of $M$ represents the set of all possible derivatives of maps $R \rightarrow M$, and the cotangent bundle of $M$ represents the set of all possible derivatives of maps $M \rightarrow R$. They are dual to each other.

I hate to ruin such a nice terse answer, but I might as well describe how I think of the tangent and cotangent bundles. I have a personal prejudice for using only freshman calculus and basic linear algebra as much as possible and avoiding multivariable calculus. So here's the way I see things:

The idea is to build everything using only linear algebra and the definition of the derivative of a real-valued function of one real variable.

So for me you have to first define the tangent bundle as the set of all possible velocity vectors of parameterized curves in the given manifold. The first observation is that if you fix a point in the manifold, the set of all possible velocity vectors based at that point has a natural vector space structure.

Next, given a real-valued function on a manifold, you want to define its derivative. Well, if all you have is the 1-variable derivative, then the only thing you can do is to compose the function with a parameterized curve. Then you observe the following: The value of the derivative at a point actually depends only on the velocity vector of the curve at that point and is a linear function of the velocity vector. Therefore, the set of all possible derivatives of a real-valued function is naturally dual to the tangent bundle (viewed as the set of all possible velocity vectors). That's the cotangent bundle (the set of all possible derivatives of real-valued functions on the manifold).

This for me is a nice coherent story that I can tell (and remember) without using any mathematical symbols at all but also one whose details can be fleshed out in a straightforward manner.

share|improve this answer
The question is presumably about deeper geometric meaning and not about how we come to the definitions. This answer is just explaining the well-known definition. The power of a notion is seen really when we go beyond the most basic applications and most basic case. For example going beyond smooth case to nonsmooth varieties (where tangent cone is often better than tangent bundle), noncommutative geometry, derived geometry (cotangent complex with all its applications...)... –  Zoran Skoda Mar 8 '10 at 16:07
@Zoran: I suppose you could be right. I simply gave my usual simple-minded view of the world (which more than suffices for anything I use the tangent or cotangent bundles for). Any chance you could elaborate on what you mean by "deeper geometric meaning"? I'm always interested in learning more about my blind spots. –  Deane Yang Mar 8 '10 at 21:06
@Zoran: I understand your point of view, but I think the issue is a difference in what different people think of as "geometric". For myself, the term means things to do with distances, angles, volumes, curves, surfaces and so on, so Deane's answer is very appealing to me. I think that for the purposes of deep understanding, motivating a definition from a simple case is complementary to seeing how it generalizes. –  Gordon Craig Mar 9 '10 at 22:52
This was Saunders Maclane's favorite point of view: you get tangents and differentials and their pairing all at the same time. I think Deane is referring to this. That is, for each p in M consider curves x(t) w/ x(0) = p, and for f defined in open U containing p, we have a pairing <x,f> = f'(0). A tangent vector is an equivalence class of such x where x ~ y if <x,-> = <y,-> and a cotangent is an equivalence class of f where f ~ g if <-,f> = <-,g>. –  Robert Bruner Oct 4 '14 at 3:17

This is a triviality, but still: there is a pullback of a differential form, but in general no push-forward of a vector field. As a consequence, one gets e.g. for any smooth map $f:X\to Y$ of smooth manifolds a map of sheaves $f^{-1}\Omega^{\bullet}_Y\to\Omega^{\bullet}_X$; similar maps exist in the complex analytic and algebraic cases.

share|improve this answer
I don't understand. Why can't you push forward vector fields? Obviously, it's only onto the image of the map, but that's already very useful. –  Deane Yang Mar 7 '10 at 3:17
We can push forward vectors but not vector fields: given a vector field in the source, we have as many vectors over a point in the target as there are the preimages of the point. In particular, if the mapping is not injective, there may be two or more, if the mapping is not surjective, there may be none at all. –  algori Mar 7 '10 at 3:26
Here is a "philosophical" explanation. If f:M' ---> M is a map of manifolds and E' and E are vector bundles on M' and M resp. then for open U in M have E(U) ---> (fE)(f^{-1}(U)) since "pull back" sections: h_E:E ---> f_*fE on M, makes sense for any sheaf in role of E but "masks" intervention of non-bundle pushforward. For sheaf map f*(f_*E') --> E' there's no way to hide pushforward. Total derivative is TM' --> f*(TM) over M', wrong direction to relate with h_{TM}, so must dualize: f*(TM) --> TM' composes on sections with h_{T*M}, yields pullback on 1-forms. –  BCnrd Mar 7 '10 at 14:30
I think that the broken symmetry goes all the way back to the asymmetric definition of a function: a relation on $X \times Y$ such that there is only one $y$ related to each $x$. In the case of one-to-one functions, we can pull and push vectors and covectors equally well. In the case of general relations (ie, many-to-many "functions"), we generally can't push or pull anything. –  Matt Noonan Mar 7 '10 at 14:52
Deane, what is your definition of "push forward a smooth object"? I think smoothness is a red herring; even for set-theoretic vector fields (i.e., no smoothness or even continuity condition) or set-theoretic functions, there is no meaningful notion of "push forward" in the absence of some way to "integrate along fibers" (like a trace map for a finite covering space, or something more elaborate in case of a proper submersion, etc.) –  BCnrd Mar 7 '10 at 17:59

If you look at manifolds with singularities, as in algebraic geometry, then the cotangent sheaf seems easier to construct. In terms of modules over coordinate rings, the cotangent sheaf just corresponds to the universal module M with a derivation d from the coordinate ring R to M. For the module of the tangent sheaf, I cant think of anything easier than just taking the dual of M.

(Added later: in particular you can construct the tangent sheaf from the cotanent sheaf, but there seems no easy way to go in the other direction, suggesting that the cotangent sheaf is more basic.)

share|improve this answer

In my opinion there is no asymmetry between the tangent an cotangent bundle.

For example the universal one-form on the cotangent space you mention. There is an analog on the tangent space, namely the Euler field (I think it is called like that), which in local coordinates $(x_1,\ldots,x_n,\dot{x}_1,\ldots,\dot{x}_n)$ on $TM$ is given by $$ E=\sum \dot{x}_i \partial_{\dot{x}_i} $$ (the infinitesimal generator of homotheties). Actually it's better to think of it as a relative vector field along the projection $\pi:TM \to M$ (i.e. as section in the pull back of the bundle $TM$ to $TM$). Then it has the universal property that if you restrict $E$ to a section $s\colon M\to TM$ you get back $s$. Just like in the cotangent picture. To make the analogy more complete observe that the universal one form on $T^* M$ can also be seen as a relative form along the map $\pi\colon T^*M\to M$.

Algori mentions that there is a pullback of forms but no push forward of fields. That's on the level of sections of these vector bundles. But if you look at the level of the total spaces of them you find that there is a "pushforward" $Tf\colon TX\to TY$ (the tangent map) but no analog map between $T^*X$ and $T^*Y$ in either direction. So that balances the apparent asymmetry.

It's more of a yin & yang.

share|improve this answer

Well, the cotangent bundle is not "more natural" than the tangent bundle (but this obviously depends on what you mean by "natural"!). It simply has "more canonical structure" associated to it - namely the Liouville one-form that you mentioned. This comes from the fact that the cotangent bundle is dual to the tangent bundle. Hence you can take a tangent vector to the total space of the cotangent bundle, hit it with the differential and get a vector on the manifold you started out with - this vector can now be paired with the basepoint of the tangent vector you started out with, giving you essentially the Liouville (or canonical one-form).
In contrast, there is no natural way to pair vectors (unless chosing an inner product); furthermore taking the cotangent of the projection reverses the direction of the mapping (it is "contravariant" in the sense of category theory).
Moreover there are also interesting things about the tangent bundle that the cotangent bundle does not have - vectors! These vectors can be integrated to flows (at least locally) and allowing you to deal with dynamical systems on the manifold! This is not possible for forms!
But of course, differentiating a function gives you a form (this can be checked, for instance, by looking at the transformation behaviour under chart changes). More generally the (principal) symbol of a linear partial differential operator is a (homogeneous) function on the cotangent bundle. That's also an important point (and causes the cotangent bundle to pop up in analysing PDE).

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Just as a side remark, when dealing with geodesic flows in dynamical systems, it is more natural to think about these flows living inside the cotangent bundle because they become automatically symplectic, which is a nice (and "rigid") structure to play with: Lyapunov exponents are symmetric with respect to the origin, etc.

share|improve this answer

There is an ``asymmetry'' already at the linear algebra level: given a (fin.dim.) vector space $V$, you get a canonical indefinite pairing and a symplectic form on $V\oplus V^\vee$, while you do not get these on $V\oplus V$.

share|improve this answer

The canonicity comes in terms of the symplectic structure. On cotangent bundle there is a canonical symplectic form that is independent of the hamiltonian where as on tangent bundle the symplectic form is dependent to the lagrangian.

Or put in another words because the cotangent bundle itself is already built from some 1-forms attached to each points, it is easy to build a symplectic from the cotangent bundle itself while since the tangent bundle is made of tangent vectors attached to each point, you need the help of a function to build a symplectic two form on it.

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MARIETTA — Cobb Police arrested a Marietta woman Thursday after police say she used a radiator hose to steal gas from the Atlanta Gas Light Company for 18 months.

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MIAMI (AP) — A Florida man choked to death after downing dozens of live roaches during a contest earlier this year in which the grand prize was a python, an autopsy released Monday concluded.

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Friday, January 18, 2008

John McCain and illegal immigration

He now says he's come around to what Americans want. He says secure the border first before.... what? dare we call it amnesty? John McCain certainly has come around to the notion that Americans don't support amnesty, but it seems his actions are to only define the word so as to desperately avoid admitting that he still supports a form of amnesty for illegal aliens.

What else can his constant rhetoric of not wanting to tell an American soldier that his mother is being deported, mean? It would seem John McCain has a reflexive longing for amnesty in some form and has learned admitting such is not a way to win votes. It certainly doesn't help that when critics disagree with his defining what he supported as not being amnesty, the senator and his supporters, rather than stating we simply disagree, instead labels us as liars. That sword can cut both ways sir.

It would seem that help for John McCain on this issue will not come from a scorecard compiled by NumbersUSA.

Sen. John McCain (R-Ariz.) scores the lowest overall. The ratings are based on how well a candidate's immigration stances would protect American workers, taxpayers, communities, infrastructure, individual freedom and the environment.

McCain is rated "abysmal" on amnesty... If we really want someone strong regarding illegal immigration, we certainly don't want a recent convert in words only, who also uses rhetoric that undermines the supposed conversion. We need to also reject one who has flipped dramatically from saying anti-illegal immigration legislation is un-Christian and un-American to saying all illegals will have to leave the country under "their" plan. I guess God decides things by the flip of the coin for that candidate.

This leaves us to consider Fred Thompson, who NumbersUSA rates higher than all the other candidates.

...according to NumbersUSA President Roy Beck's Presidential Grid that rates each candidate in 16 immigration categories, Fred Thompson scores the highest. (source, thanks to Ace)

Also, as I've noted in a previous post here:

A Fred Thompson type of plan is already showing it's effectiveness at the state level.

Remove incentives for coming here and there is no need for deporting them all, which no major pro-law, anti-illegal immigration proponent has pushed for anyway.

Fred Thompson supports proven means to reduce illegal immigration. He's presented his views with more than mere sound bites and without supporting amnesty outright or by foolishness resulting in sanctuary for law breakers. This would be part of the reason that conservative Iowa Congressman Steve King endorsed Thompson. This, among many reasons, is why I still support Fred Thompson for President.

Hopefully South Carolinians will carefully consider the candidate's records on the issue of illegal immigration, who has merely pandered at the last minute and who has actually presented a plan that has already met with success, when they vote this Saturday.

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The information and opinions expressed on the following -- commercial programming are those of the hosts and their guests and do not necessarily reflect those of this station. In around me. -- -- Or. Yeah. Now there we're bad. Good morning and welcome to the program this morning. I want -- well commute into retirement planning strategies. Have by way of introduction my name is Edward are there -- I'm from Overland Park, Kansas my offices just off by 35 at Santa Fe and always thought. What we focus on an organization. In the business is primarily set aren't. Offering reasonable. Sustainable. On practical solutions for retirement. That crosses my mind sometimes when I'm talking about retirement that. You know maybe that's a -- such a subject. How about instead when we speak about retirement we talk in terms of spending the money. I -- say -- foray comfortable and enjoyable period a time one sure not reporting and your job any longer. You know if you're. Taken a cruise -- -- redoing the kitchen and gardening. You've got an RV in your cruising about the country and seen in all the site she always wanted to see. That should be part of retirement planning but it isn't really a drab subject it's supposed to be something that's fine. And something rewarding for your hard work after all these years on the job. So I think terrorism a mistake can focus when we talk about this. Amongst people in that they tend to think in terms of they have to have a certain number of dollars like a dollar goal. To meet -- there needs. And and that's not an irrelevant thought that realistically. -- Don't you really want a reasonable. Sustainable and practical solution. To having the income your going to need when you don't have a paycheck every two weeks. It's very very simple process. To do -- the thing that we try to show in the our show which is retirement planning strategies. Which and I think there's a lot of back up for us on our web site if you are comfortable logging -- and that is it safe money. RX stock come. SA FE. MO NE YRX. Dot com if you logged in their he'll find a number of different tabs can are for you information about. Approaches. Theory is strategies that can help you. To reach. Your sustainable spending. Needs in retirement isn't that a prudent thing to do. So we're dedicated. In our business to the client that's nearing retirement. And of course those who have retired. And I wanna focus on this because it is in a sense a subset of the population. Our clients really that there needs. Are different. Than what they had at the time when they were our in an occupation. And cashing a check. And pay in the bills. Most of the people that I talk about they have or talk about in this segment. They wanna speak about what risks they might have been their investing habits and many bring -- -- turn over the they've suffered through losing year since losing. Multiple year periods in the stock market. And what they voiced to me very clearly is they'd like to have security. Unfortunately. Often people come back to a dollar amount of money that they need for security. Is that worth. Considering is irrelevant it is. But really what you need to know is from your money and expected on your lifetime. How much income do you expect you'll need periodically. To pay the bills pay the taxes by the gross shrieks and have some fun. So -- is the only approach. A person can take. To step out into a casino and gay and bowl all the time with Wall Street. I want to say no. And I ask you to get up stop. Get a piece of paper. And won't give you a phone number on web site. Where you can contact us and just look in two and another. Alternative method. To funding your retirement. To finding your income needs. To providing yourself with the fire and you anticipate. As you sever your relationship with your occupation. It's benefits to be it's up today. So we've got to help you in a way that's reasonable and rational. Which quoted last week. From AM magazine are actually was from four -- Where a gentleman gave a breakdown on a 6040 bond stock allocation. Going into retirement and drawing 4% a year from the fund. And he quoted. As statistically. Over a thirty year retirement. That process had a 50% chance of success. What we're suggesting instead is -- to take the bull by the warrants and planned for your retirement by planning your income. Rather than. Investing in such a way that you make enough money to offset your losses. Less fees. Does that sound a bit different. Really those because what we're talking about our steps. That are concrete. -- contractually guaranteed. Now we often talk to people who come into us and may have a great fear. Of losing money in the stock market. In many of them have done it time and again. But it seems as though they know rationally understand that there are to alternative methods. To handling your money. To create interest. To create. -- down a full. Period in retirement. Why would -- speak. I heard about this today and a gentleman called me from park -- Last Thursday I spent some time talking from with a gentleman on the west would. And in Westwood and on Saturday an engineer called me. And he was in Kansas City, Missouri we had quite alarmed discussion. Each of the three people started their discussion. And put a lot of emphasis on that they were anxious that they had anxiety. About their life savings. Because they were in the stock market they wanted to now. Like can -- what can I help them what what can I do that should ease this tension. The stress that they have. So we went through it individually. The conversations. Ran of course based on what they wanted to know not what I had on my sermon. We talked about there -- means and there were quite different some had. Extended family is that they wanted to leave a legacy to. We actually are one of the couples has no children. They're sitting in a spot which if they don't for renal lose their money they've cut money to live on the really super seniors already. So why is there and and why is though this -- deep seeded handcuffs mentality. That in order to make it you've got to be directly investing in the stock market. I spent a lot of time thinking about this. And I've thought about it for you person and one of the reasons I believe. That it's so ingrained. His because. There's a generational. Shift that happened with baby boomers. Baby boomers. Started working. In jobs that most of the time didn't provide them with the pension. It was one of the a big generational shift from the people in the Henry Ford generation. And the Silent Generation of World War II. Most of those people. In the earlier generations. When they retired. They had lived a little more modestly than we do now and when they retire though they had a guaranteed pension that paid them for lifetime. So let's think about that they had they had a comfortable situation in their retirement they saved money. They had social security. And they had a pension. Sounds pretty good doesn't that. Because most people I talked to today I mean the vast majority aren't gonna have a pension. So they had a pension that came in every month. And just swat it just so happened at that pension paid them the rest of their life. They had savings they can dip into aunt and Uncle Sam gave them something. That a Social Security check. That came every month until late. Now there was a generational shift. The baby -- started taking jobs. That do and that did not even an anyway offer pension. What do they -- on Staten. Here's the paradigm shift. They received. An opportunity to participate in a company sponsored 401K. Savings plan. Is that bad. I don't think so. But when they got the 401K. And those original days many people got a high contribution. From the company to match their. Deposits. And today. My most recent interview with someone a gentleman told me in -- tech business. That he's only getting half a percent match and anything he puts in his account. So. Not cut the concept I'm basing this on is as you have the opportunity with this 401K to shoot demand. You get to put the money in their conveniently. It comes right out your check through the HR department a plan administrator puts an and a bunch of times. And if things go well -- feeling like you're on high cotton that's just the fact. But it's a rollercoaster. And what are you lacking -- You don't have the pension. The guarantee. You still get Social Security. But what are we hear about that all the time it's underfunded and the government is mismanaging it -- governments tapping the phones. Demographics aren't there's a lot less people pay union whose social security. And there were in past. Generations. So now everything is hanging by the neck of the forewarned K. Let's go into detail why did a company start offering your 401K. Because that's about the cheapest approach they can do that the most. Inexpensive to the company. Have any approach they can take. -- compared to a defined compensation. Sorry a defined contribution. And or defined benefit plan which would be a pension. There's literally. No responsibility. On performance on your company your employer. And now that the benefit has spent. Back down where you're not getting the matching money at the percentage that people did in earlier generations participating in the forewarned -- They're completely off the hook. They're basically just doing a payroll service deducting them money. Now. This is important to digest is. The previous generation. The Silent Generation and Henry Ford generation when they retired they got three payments for life. Out of a pension. They also got up payment for life. Out of Social Security. These were things I can hang their hat on in insured. It enabled. A comfortable. Stress free retirement. -- can anyone out there in the audience after weeks and weeks of this define some thing. That you put money into. Through the year sure working and when you retire it won't pay you income for the rest your life. Any answers out there. We'll take your piece of paper and write this down and annuity. And in new OT here's a device that you deposit money and it draws interest without being taxed. Currently. And when you decide to take money out you may take a life time payment of income. So. The pension plan and so defined benefit plan. And the Social Security program. To a sense. Those are annuities. Do they not pay you annually and income for the rest your life. So what I'm trying to. Portrayed you today as those of you that feel that you're on thin ice because your directly. Invested in the stock market. Would it benefit you at least psychologically the things that you had income for life. And that your money was protected from the volatility of the stock market. If so. My -- that are -- and I met 9137688090. And our purpose. Is to protect the money you saved in grown. So it's here to provide for you now that you are in retirement. We should talk. Give us a call and will be back with more ideas. Yes I can. Suddenly. Yes I can. -- -- -- -- Welcome back. I hope we caught your attention on that previous segment but just to -- look forward we're just saying that. When people retire. Are they not more comfortable having a steady stream of income. After 25 or six years of doing this I can tell you. That people are most comfortable in that situation. And there are a lot of things that can be applied to that there can be inflation benefits add to that. There can be benefits and add extra benefits extra payment to you if you have to have long term care. Treatments. Care. And so there are many things that go along with this but I'm just saying that what happens now. And and were caught were reaching out to you here on 166 DA MK NBC's business channel. We want to talk to you in our office quietly privately. And with. Some prudence. About the idea of protecting. What you have. Win. We're having a huge casino like party going on in our country. With the government manipulating interest rates. Buying debts. Running up seventeen point four trillion dollars in debt by now. There are a lot of things that are gonna. Potentially upset the apple cart. We've been hearing now for some time that the Federal Reserve at some point was gonna stop buying as many bonds -- Stop manipulating the interest rates low to try to put gasoline into the economy. And asked they've started to move away from the easy money policy. We expect to have a little impact your perhaps the stock market won't PS. Exuberant. Shall we say. But are there other impacts that you might be concerned about. As we start to change. The behavior of our currency the world reserve currency of the US dollar. At least for now. As we start to change its parameters and its interaction. In the lubrication of economic activity. What's gonna happen other currencies around the world. Would you expect them to have some fits and starts. What about Turkey. What about Brazil. What about Argentina Indonesia. And our giant partner. China. Things are starting to. Be shaken. Little earthquakes. The Japanese are fully committed. They're valuing their currency there and export economy sounds like -- a good move does net. They're following our lead. At a mathematically more intense way. So if you're fully invested in the stock market let's remember. There's a difference between saving money for retirement and being an investor. When you're invested. You've put your money at risk. You have paper in return for your currency. And that pay per. You -- the right to participate. In the values of those stocks or mutual funds. Isn't that true. And he really don't have money -- cash out of the -- And as the market goes up and down like it did in 2000 to 2002. On its big dot com crash. In 2007. NA into nine with the housing crisis and loan mortgage problems. People had really large jolts. If you're out there in your sixty years old right now 55. 65. And you're in the investment game with all the changes that are happening politically and with the world currencies. There are going to be. Some very. Uncertain times. With your investments. What could you do instead. While if you put money into a savings type vehicle or an uninsured with type vehicle or a product that has contractual guarantees. You can avoid price above this mass. Is that the right thing to do. It's worth -- discussion is -- not. Is it not worth a discussion you should call us at 91376. Say 8090. And we'll consider your outlook. And what you want to do. And what your concerns are. And we want to show you methods. That may contribute. To pay more consistent. Pass to retirement. One that has a higher possibility. Of stability and security. Would it not be a good idea at 556065. To have some predictability. On what you're going to have left in your account to spend. As she retire. Do any of you remember friends. Who intended to retire in 199819992000. Who went through that huge crash and ended up working for many more York's. Because suddenly their golden now instead. Was cracked. Or crushed. Now I'm going to say. But I believe there's a subset of people that are gonna listen to this radio program and they have particular or skills. They have specialized education. Or a certain level of awareness where they're able to work with markets in terms of timing. They're able to understand how to make money when the stock market goes down. As well as up. And for that person. We're glad journalists staying in with us pass our information along to a friend. But we're not trio. We are looking for the sub -- of the subset of people who say -- probably have enough to be retired. I just don't wanna fool around -- And we've many times gone through the process of discussing. With clients and here on the found. And here in the office we've done that many many times have people where we discuss. That if you're not comfortable with the exposure -- just don't understand that you have an option. How would that option play out I mean most people I talked to them about to say well. I'm in the stock market because if I put my money in the bank I'm not gonna make much interest and that's true. If you push -- money in the bank you're not gonna lose a if you put your money in the market you might lose it but she might make more money we're trying to hit a middle ground here for you. Where you can have your money in May account that is insured and contractually guaranteed. And is set up with the intention of providing new in town. And I cannot describe it on the phone as well as I -- in person. But in this safe secure. Contractual guarantee account will also earn interest. Linked. To the movement of the stock market. And the good news about that is that if the market is up you'll earn a percentage of the gain in the market. As measured by an external index. Of a group of stocks. New -- amongst them. However. When the market declines and it well. I'm certainly not timing that are calling it out to you I have no special insight here. But it when the market goes down. Your account. Will not lose money. You will not and write this down he will not lose the money you put in your account. And you will not our -- will not lose the interest that you've previously. Earned on your account. Put that juxtaposed to -- our own experience with your mutual funds. You might get a fifteen to 20% gain any -- you might get 7% over several years. You're experience will very. And I'm speaking to you about your experience. I am not telling you about your mutual fund performance. I'm saying consider how your performance is dead but also consider. -- three or four years out of the last twelve. Where the market has declined. And you've seen a decline in your total balance of your account. It's disruptive. And it's not always appropriate for people who -- and be safe. Stable and predictable for income in retirement. Would you agree and if you do. Look up some of our options are unsafe money. RX dot com. And I'm always -- Pushed by those -- the radio station and the listeners that I have. They're calling and they say make sure everybody knows it's best they pass. AM oh in he why our tax stock car so it's a prescription for safety. Apparently no matter how hard I tried to turn NCAA that it sounds as though once as saying SA ZE. It is SA FC. Now -- have a few other topics we're gonna bring in today but I want to bring up some things that have that are really addressed to me by. People come and serve my conference table and what they're asking about are the specific. Inputs that they have from other advisors. I think most advisors throughout their working really hard to -- the best they can't. We're just in a sense giving you a different view of the same. Turmoil a few well. I'm -- our -- and again we're at 913. 7688090. More in just a moment. On this day. This quality you -- it's. Days who. Then it's a feeder -- economic those like me go I know so to the company's. Through welcome back we're gonna pull forward. I thought. Were going to try to bring end to the conversation. Be. Question that I had from a gentleman and park -- In the essence of what I'm saying here going back to the last two segments -- were trying to say -- There's an alternative between. -- besides I should say going into a bank. In order to make your money safe. And gaining no interest. There's an alternative. That fits between. Going to the bank as I mentioned. And going to a brokerage house. Or leaving your money in a 401K. On the rollercoaster. Of the stock market. That's what we're talking about where we're talking about accounts that are safe. In that the market won't cause you to lose money. That relates quite well the bank. In on the other hand can credit you higher interest in the bank. By indexing to the stock market so the question. That I had that I think -- in a sense. In a lace sand springs up. This particular thought process and this gentleman -- fill up. Said why would a -- in a new a team be suitable for retirement savings. Well ominous -- they're -- that's. What and annuities for. Retirement savings. But I'm not I'm I'm just saying. When the question stated let's answer that right there. It's rolling into an annuity is not for somebody thirty to start so that they can take money out to buy a Porsche at 45 okay it's. It's really drove -- to be used after the age of 59 and a half. This gentleman went on to say I have never changed my 401K holdings. In several years ago I was terrified that's his word during the crash of 2007. And nine. Today the accounts are way way up. So almost exhilarating. But. If I look at history they're just now were they were. Back in 2006 or seven. So in this case. I'm assuming he's already retired so he's not adding money. To the account so he's just looking at what he put -- and plus the -- us last the bad years less the fetus. Okay. So why would be why would an annuity his question is why would that be a choice to consider. Well. My answer here is somewhat age specific remember studies show that people become. More protective. Of their life savings as their birthdays out up. At age 55 sums the study show that people or two to five times more risk averse. Than they are earlier in life. And did you know that the same study showed that at age 65. The individual may now be five to ten times more risk averse. And I don't mean to tell you it's 75 the number -- Quite exotic -- if you well. So the point is is that it does that make sense I'm speaking here and here the listener does that make sense to you is it rational. Is -- common human. Sense that as you get older you're more conservative with what you have save for retirement. I don't think have to push -- hard from that point. So it makes sense doesn't and an older ages it's less likely. That we would have a job. Long time employment. We may have in fact Pasteur peak earning years. And there's a concern now you look they're gonna have cost a living the rest your life. -- you don't have a check every two weeks. And seniors have to make due with what they've accumulated during their years on the job. Now I think. If you're of the same mind you should call us and you have to get up and do something about it for us to talk to you. All you have to do. Is pushed the ten digits on your found a 9137688090. And -- her. Earning the number of people on our office will be happy to talk with you about. Once you've accumulated the money you're gonna need for retirement. Do you really have to stay in the stock market came. You do not. You can take an all -- and put it in the bank. But she may loose. Some traction there if inflation as high. But an annuity contract. With a reputable high solvency highly rated insurance company. -- guarantee. They won't lose your money. That chiller and positive gains in the times at the stock market is good. And that you'll never lose money back if the stock market has. A downturn. Further. You can. With make a selection if you prefer that will provide a guaranteed return on your money every year regardless of the stock market's performance. If you're an arrest in six and a half percent guaranteed for fifteen years. There must call. -- I don't think that's inappropriate and let's put it this way. On the ones that have 456%. Guaranteed to you might actually do better than that. If the market has a good. Run. We've had a whole pile was statements command that are double digit on our clients. In recent weeks and months. Because there sure was a good you're in the stock market the difference is going to be assist some point in time the stock market's gonna go down. And our clients won't lose back what they've gained. Whereas. People in stocks or mutual funds three T asked they're likely to see a decline that's earned net asset value of their camp. Is there anything wrong with investing for retirement there is not. But I find that a lot of people just flat aren't aware that they can. Save money NA insurance product. And use its accumulation factor. To safely produce a handsome return with out the risk of direct investing. Most are just think it makes cents. So this collar. When he. Was leaving a message said he was terrified during the crash of 2007. And nine. And he mentions. That even though he was pretty happy with the growth. From 2009. Through their early part of her late part of thirteen. He realized when he looked in his statements and went back four year -- That the balance of the account was just now. Passing where it was in 2007. How many of you have repeated that now at least three times in your life. If you you know if you do not change. What you're doing. History says it may be repeated. We hear that in a number a different way news. So we're just suggesting given us a call because if we can help you understand. How you kid grow your money. Based on stock market gain without the rescue. Then you may like that alternative. So had another point that people have brought up with us is that. If I have a 401K. I've never rolled it over. I don't wanna do that because what happens if I have to pay the taxes on that money. Well you can always do an account. Switch a lateral if you wanna call it that. And roll that over and a fixed annuity and aren't any taxes to pay because of the proper filings. With the I arrests. That allows you to roll out of an equity account -- 401K account. In two. A deferred annuity you and that is gonna turn it into a traditional IRA. And you will not have a tax event to do so. You can always consult with your accounting professional there. And we recommend that we like to work with the accountants so that we keep everybody on the same page. Now I've set an annuity several times I'd like to flesh out another point. There are two kinds of annuities essentially. There's one that's called fixed annuity and one that's called -- variable now I think. And a variable annuity. Is primarily any deferred account a contract was an insurance company where the money. Is. Placed into variety of mutual funds. Again if you're an astute investor. And want to manage that and you want to be up on the trend she might do better with that. We are in our office specialize in used in in using the fixed type qanooni. And the reason for that is is the money goes in the insurance company and does not go out into mutual funds. Instead the insurance company uses options. To track the movement of an external index of the stock market be that the S&P 500 of the Dow Jones for the NASDAQ. And today we have once -- have all types of creative accounts. Where they measure the performance of an underlying financial instrument. And the change if positive the centrist. So we're out the technicalities now we promised to come back on the other side and talk more. About how this should feel to you work with us because your comfort. Your stability your predictability. Is what we're working for. And when we provide that. You might recommend this to a friend and stay with us and provide to have you with us today so -- every time. Thanks for staying with -- my name is set Hardenne and Barbara number here and a moment. Our web site is safe money RX dot com. In your listening to retirement planning strategies -- -- BC's business channel. 1660. AM. I think I got out of the weeds on that last segment I've. I don't know I mean maybe I was speaking to a group of engineers are accountants are soft and and view -- when a commanding an -- -- clear understandable representation. Of how these things generate interest. These things being fixed annuities. Indexed accounts. You're welcome to come in I've been told by many. That they've heard this sort of thing before but I it was the first time they understood how they actually worked. And I'm proud of that because suffice it. Matter of fact that one of the first that this is how I'm just chatting up now again this is sort of how hobby in a way but. One of the very first things I do if you came in bill or Nancy you're. David and came in and talked to me as I wanna know what kind of work you did. What your responsibilities. Were -- recent. Education in hand. And I'll tell -- the reason for that is deserved it it is and how bad motive. The motive there for me is it moral last -- me a sense. Of how I might explain something to you. Because our world now so specialized. That we all really are experts are weighing in what we're doing. I mean a nurse these days men have a lot of nurses than they work and operating rooms. They do all the work in the operating room so to speak. They don't get to make mistakes I mean talk about highly trained. I have engineers. And were driving over their bridges. They're hanging buildings on cranes they design around us. And I mean the there's a tremendous level of professionalism. And all the things we do. So more and I'm speaking with you I am trying to take my specialty my sliver that I -- A professional and and I'm trying to. Modify the explanation. To the point. Where it's consumable. Understandable. And something that just what makes sense to you. Well now I think that's a little different. And the reason I say that is because. Very often I have people come in my office and say it's the first time they've talked about their retirement income money. They're retirement investment in town with anyone who didn't sit on the other side of the desk and talk down their nose at them. I'm very. Devastated to hear that that's what people's opinion would be how many of us in this industry. But I think you would find a more accessible person. In that I'm really going to try. To find the best way. The best analogy used the metaphor worse. The graphics. That show you the best. Most consume mobile understandable. Concept. Of what we're talking about -- a funny word to some people are concept orient and some people or detail oriented and I'm looking for that when I'm talking to you. So if you're concerned about keeping your money safer than it is in the stock market or you're. Concerned about earning more interest and you weren't the bank. And toss employees are you concerned about tax consequences. I'm not an accountant but our work with -- now five firm that I have a lot of information there. That we want to get together with you and help you figure out what you might do to protect yourself. I wanted to. I can be a little accessible here and are heard much commentary over the sort of thought that I portrayed it two or three times here on the show up. I want you to think about going. And getting I have taken a nice trip I mean. It's been a brutal winner in Kansas City pretty much. Analysts say just for the heck of that you went out to the desert. And some people love the desert and some people down but in February or January or December. It's not a bad idea when you consider all these twenty degree days that have fifteen mile an hour winds. So on our trip to the desert we just haven't stopped in the Las Vegas. And wow. Is that not an amazing place it's almost like a fantasy land out there in the desert. It's beautiful. It's luxurious. Every creature comfort. Amazing hotels and services golf tennis. Casinos. -- when you have any need you want. For a dollar you can get it out there. And actually a lot of it properly planned this free has net. I mean you can. Run -- lot of nine dollar buffets with primary a bonnet and you can eat -- while I mean if you're outside what I am I'm not a big gambler but I know if you're -- and they don't hesitate to bring a few drinks on the house. So you can have a good time out in this amazing place but when you go to Las Vegas. And you're going there and you get into gaming. For slots -- Tina our black -- sports betting your poker. When you get out there. You and I really know if you're realist that they didn't build that place for you to win at two games today. I mean. You have to be flat. Proficient and have a good run a -- to come out even or ahead. Although. We always hear those stories don't -- The only way I get out of there is just say well I'm only gonna lose this much -- when I do I'm done. So clearly. They went a lot out there to build all out amazing complex in Las Vegas. Now can I make a comparison there. If you wanted to do that sort gambling. Then. Probably Wall Street. Is the place she wanna invest. Because it is up and down. Up and down and happened there are. And when are things good ideas -- of people getting good ideas about buying things don't they often do that after a stock -- garner out. Or because a stock has -- up. And there are so many changes. In the world and so many changes with our global markets. That it's become an amazing. Complex. Event to invest for retirement. Now let's throw end don't ask somebody gets under their seventies and eighties. 60s70s. And eighties. Is there any chance that we might be a little bit behind. Those -- most proficient at the game of the stock market. So if that's the case. Would you rather move to something that's a little bit safer. All over the last couple years we've had a heck of a run in the stock market the -- now for example. Then in nineteen no wonder in 1903 that the Dow Jones fell 46%. And it took two years for that to recover. In just three years after that in 1906 to 1907 the Dow fell 49%. And that time it took -- nine nearest to get even. That was a pair of corrections that was right at 50%. In one decade. Then we had. 1916. To seventeen in the Dow fell 40%. 1919. Didn't 1921. The Dow fell 47%. And then the big 11929. To 1932. The Dow fell 89%. And that's not the bad news. When it fell eating 9%. It took 22. Year Ers. To get even. 22 years so in the world in World War II. So I'm asking you know if you've won a game and you have the money you need to spend to go to Las Vegas. And Wendell won't lose a little flask of often on a planned trip does that make sense. To avoid the potential losses. That the market. Can have that would directly affect how well you actually enjoy. The years you have after your employment. I think -- under any sense it makes sense at least discuss sure options. Outside of the old drilled and 401K thinking where the only thing you had were mutual funds. And the only thing you had were equity is embarks. There is an alternative that will be attractive. To at least some of the. So give us a call 913768. DD ninety. And will be there for those of you who would like to have stability predictability. And safety. In your retirement years that's why we exist. Sent our Dan Collison 91376. -- DD ninety -- around me. When you. Yeah.

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