would be like
taking a monkey to watch a ballet, hoping that it would learn to
dance.
Jim Bromer
On Thu, Jan 24, 2019 at 7:04 PM Steve Richfield
wrote:
>
> Jim,
>
> I programmed DrEliza.com in MS Access SQL, that provides the ability to
> program SQL functions in full Visusl B
ything short of that is
message-in-a-bottle AI.
Jim Bromer
On Mon, Mar 18, 2019 at 1:59 PM Boris Kazachenko wrote:
> We must define a process in which language can emerge from incrementally
> complex encoding of analog sensory input. Anything short of that is a
> cargo-cult AI.
>
>
> On Su
chapters I think you should make sure that you include a few worked
examples. If there is anyway I could help you without working full time on
the project, let me know.
Jim Bromer
On Sun, Feb 24, 2019 at 11:46 PM Linas Vepstas
wrote:
> Attached is a PDF that reviews a relationship between symb
to you?
Jim Bromer
On Sat, Feb 23, 2019 at 3:39 PM Nanograte Knowledge Technologies <
nano...@live.com> wrote:
> <https://mathinsight.org/definition/network>In other words...the purpose
> should be functional RNA.
>
> Now, is an AGI blueprint justified?
>
>
I wonder if there could be an open source where people or teams might be
able to try their own ideas without being persuaded to pursue someone
else's overarching theory?
Jim Bromer
On Sun, Feb 24, 2019 at 12:09 PM Mike Archbold wrote:
> On 2/24/19, Matt Mahoney wrote:
> > Colin
to the data objects but to the class and so it was a double indirect
stuporific. The double indirect stuporific is probably the standard these
days because operating systems get their position because they are so
superior in multitasking.
Jim Bromer
On Sun, Feb 24, 2019 at 12:50 PM Linas Vepstas
wrote
be based on words used in sentences not just word occurrence rates. It
would not the same as basing it on general knowledge in some way.
Jim Bromer
On Mon, Feb 25, 2019 at 9:45 PM Linas Vepstas
wrote:
> Hi Jim, OK thanks! I don't know what you enjoy, what you are good at. So
> I don't kno
e more complicated
'things' which can be 'handled effectively'.
Jim Bromer
On Wed, Feb 27, 2019 at 10:50 AM Matt Mahoney
wrote:
> The long awaited sequel to AI4U. :-/
>
> If I had a an idea that I thought would greatly accelerate AGI, maybe I
> would publish it so that when others de
. The nature of *limiting* ambiguity of a symbol
(or possible referential signification) does not seem to be a very powerful
tool to rely on when you are trying to stretch the reach of current (or 30
year old) ideas to attain greater powers of 'understanding'.
Jim Bromer
On Thu, Feb 21, 2019 at 2
nswer to *almost any*
situation. From my perspective, we are not playing the same game. I should
not write this kind of crap. I should try to understand the ideas that you
were trying to describe and leave the personal attack out. But I really do
not understand what you are talking about.
Jim Bro
ible in AI. And your views on this subject are going to be
very helpful to me personally so I am looking forward to reading it.
Thanks.
Jim Bromer
On Sun, Feb 24, 2019 at 11:46 PM Linas Vepstas
wrote:
> Attached is a PDF that reviews a relationship between symbols and reality.
> Depending
Linas' introductory text on a formal mathematical definition of
interpretation and how it is related to interpretation.
Jim Bromer
On Wed, Feb 27, 2019 at 12:27 PM Jim Bromer wrote:
> >>Or maybe others would just ignore it because ideas are cheap and
> developing them is hard work
ntent
of a statement or of an event?
Jim Bromer
On Fri, Feb 22, 2019 at 9:51 PM Jim Bromer wrote:
> "Such is the basis of critical thinking, to derive the correct answer to
> every situation."
>
> No, that is not the basis of critical thinking. Critical thinking refers
> to, i
.
Jim Bromer
On Thu, Mar 7, 2019 at 7:24 PM Robert Levy wrote:
> It's very easy to show that "AGI should not be designed for NL". Just ask
> yourself the following questions:
>
> 1. How many species demonstrate impressive leverage of intentional
> behaviors? (My ans
that will one day take
a giant step over the present-day hurdle of complicatedness.
Jim Bromer
On Sun, Mar 17, 2019 at 10:01 AM Jim Bromer wrote:
> This argument from Robert Levy is not quite right, in my opinion. While
> most animals do not have a sophisticated language, it can b
This was really interesting.
Jim Bromer
On Sat, Mar 9, 2019 at 10:09 AM wrote:
> Do Neural Networks Need To Think Like Humans?:
>
>
> https://www.youtube.com/watch?v=YFL-MI5xzgg
> *Artificial General Intelligence List <https://agi.topicbox.com/latest>*
> / AGI
be able to detect similarities and differences in
different kinds of symbolic sub-nets that cannot be anticipated before hand.
Jim Bromer
On Sun, Feb 17, 2019 at 12:33 PM Jim Bromer wrote:
> The most significant advancements seem to be made by using NNs with
> categorical feature det
of features in GPUs is missing because games operate on
the principle of projecting the game space onto the visual output, not the
other way around. (Sorry I don't have time to edit this to make it more
readable.)
Jim Bromer
On Sun, Feb 17, 2019 at 9:47 AM Stefan Reich via AGI
wrote:
> Is that an anti
These days a symbolic system is usually seen in the form of a network - as
almost everyone in this groups know. The idea that a symbolic network will
need deep NNs is seems like it is a little obscure except as an immediate
practical matter.
Jim Bromer
On Sun, Feb 17, 2019 at 8:27 AM Ben
process that I cannot
see why it should be discarded just because it would be relatively slow
when used with symbol nets. And, there are exceptions, GPUs, for example,
love projecting one image onto another.
Jim Bromer
--
Artificial General Intelligence List
Human beings make machines that are more powerful than they are, and
can do things that they cannot do.
Jim Bromer
On Tue, Feb 12, 2019 at 10:36 AM Matt Mahoney wrote:
>
> On Sun, Feb 10, 2019 at 7:46 PM Alan Grimes wrote:
> > I've read about half a book that I highly recommend
re
related and how they shape (or direct) meaning and how we can solve
problems. It is this construction mechanism which will give us insight
to more human-like intelligence, even if the answers are not entirely
correct.
"
Jim Bromer
On Wed, Feb 13, 2019 at 1:25 PM Matt Mahoney wrote:
>
&
I just realized that Turing talked about a computer that could play
the imitation game. So if a computer program was that smart it could
easily imitate a human being. A slight change in the Turing definition
fixes the problem that you (Matt) mentioned.
Jim Bromer.
On Wed, Feb 13, 2019 at 6:32 PM
These comments by Linus seem a little stale. Have you ever made
inquiries about your recollections about what IBM said Watson could
do? Have you looked into the current progress of Watson with medical
knowledge? Expert systems were designed to make comments about further
tests and then they could
as the particular use has been previously studied. I am
talking about concepts, but the idea of a symbolic reference net might be a
little more of an objective description.
Jim Bromer
On Mon, Feb 18, 2019 at 10:22 AM Jim Bromer wrote:
> Since I realized that the discrete vs weighted argume
this only to emphasize the idea that new ideas about the
compression of computational objects may arise out of the most mundane
of tasks and we may be casually discarding some ideas that might be
useful without even realizing it.
Jim Bromer
--
Artificial
Great article. Thanks again.
Jim Bromer
On Tue, Mar 12, 2019 at 6:28 PM wrote:
>
> Exploring Neural Networks with Activation Atlases:
>
>
>
> https://distill.pub/2019/activation-atlas/?utm_campaign=Data_Elixir_medium=email_source=Data_Elixir_224
> *Artificial General Int
Although the Activation Atlas is a little misleading (in my opinion), it
has given me some vague ideas about how a symbol net might work.
Jim Bromer
On Wed, Mar 13, 2019 at 8:18 PM Jim Bromer wrote:
> Great article. Thanks again.
> Jim Bromer
>
>
> On Tue, Mar 12, 2019 at
rengths' or 'weights' in terms of the
nomenclature that we typically use - in order to understand the potential
that is in plain sight.
Jim Bromer
On Fri, May 31, 2019 at 12:32 PM wrote:
> I mean you can make a symbolic system without factors, but I guess you
> could have factors but it
It is unlikely that many people are going about it in just the same way as
I am.
Jim Bromer
On Wed, Jun 5, 2019 at 2:25 PM Jim Bromer wrote:
> When someone talks about deep learning they are talking about some kind of
> method that 'connects' weights and other functions derive
abstractions as seems useful, and then following Occam's Razor, pare it
down closer to using only what is necessary. (Occam's Razor looks like an
idealism which means it is therefore imperfect.)
Jim Bromer
On Wed, Jun 5, 2019 at 10:44 AM Jim Bromer wrote:
> I did not mean to be overly critical in
I am not sure what it is that you (rouncer81) are saying. Can you give a
little more detail to your statement?
Jim Bromer
On Thu, May 30, 2019 at 8:40 AM wrote:
> factors are important, but symbology has a strength where its known to be
> true without detail.
> *Artificia
) be expressed in terms of Boolean Logic does
not mean that it is* just* Boolean Logic. Arithmetic is something special.
Jim Bromer
On Sat, Jun 1, 2019 at 8:07 PM wrote:
> I dont want to stop this amazing imagination of yours. But I must warn
> you ockhams razor is there to dismiss
I know. If that happened squares would take me seriously.
Jim Bromer
On Wed, Jun 5, 2019 at 3:11 PM wrote:
> ha, watch out, theories can catch on whether you like it or not. :)
> *Artificial General Intelligence List <https://agi.topicbox.com/latest>*
> / AGI / see dis
to function as a whole and to eventually develop computer programs
that will show their usefulness in future AI and AGI programs.
Jim Bromer
On Tue, Jun 4, 2019 at 6:07 PM wrote:
> Ok, sorry about that misunderstanding.
>
> You need to form the model of the of the working area of the a.
can think about varying
columnar characteristics and varying carry rules and so on.
Jim Bromer
On Wed, Jun 12, 2019 at 11:03 PM wrote:
> If you give yourself infinite computation power an exponential brute force
> search of physics engine logic, contains all methods that
you for your comments Steve, because it helped me to think about this
from a slightly different perspective.
Jim Bromer
On Sun, Jun 9, 2019 at 5:53 PM Steve Richfield
wrote:
> Jim, etc al,
>
> This discussion was greatly extended and played out in the early days on
> neural
but it has to be able to narrow in on discovering what is relevant
to resolving a recognition issue and other analysis and reaction issues.
Thanks for your thoughts.
Jim Bromer
On Tue, Jun 11, 2019 at 8:33 AM wrote:
> I can understand what your saying to a degree.
> Indeed if you trained a labe
are, and this mini sampling indicates that there is
something here that might be worthwhile for me to examine partly because
there is not going to be much competition.)
Jim Bromer
On Tue, Jun 11, 2019 at 12:54 PM Mike Archbold wrote:
> This topic reminds me of this book from almost 20 years ago:
>
&
or
something. The freedom of thinking outside the box, even though it will
usually be unsuccessful, illuminates whole new vistas.
Jim Bromer
On Tue, Jun 11, 2019 at 1:23 PM Mike Archbold wrote:
> mean't "wasn't being dismissive". Typing too fast
>
> On 6/11/19, Mike Archbold wrot
The statement that unsupervised GAN's are the way of the real brain is an
absurdity. Human beings do not yet know how the brain works.
I do believe that the mind must have some way to project objects (like
images of objects) onto other objects (like other images of objects or
within an object
analysis. If that were the case AGI would be GOFAI.
Jim Bromer
Jim Bromer
On Mon, Jun 24, 2019 at 10:32 AM Matt Mahoney
wrote:
> The Turing test is a criteria for AI. It is not the test of a theory.
>
> On Sun, Jun 23, 2019, 9:26 PM Costi Dumitrescu
> wrote:
>
>>
>>
functions of varying ratios as a compression method.
Or, since I envision my (conjectured) mathematical conceptual index as
needing to use different 'recipes' of ratios between different kinds of
conceptual evaluations, it might be very useful. Thanks for mentioning this
idea.
Jim Bromer
On Mon, Jun
do not see anyway to use it effectively in
programming.
Jim Bromer
On Sun, Jun 23, 2019 at 10:02 PM Jim Bromer wrote:
> That idea did not work. You can send 1 of 6 states in 2 clock cycles with
> the method I was talking about but if you have a no-voltage state then you
> can send trina
associated with (crudely effective) compression operations. It
would be very crude but it might illuminate a problem that is (if I am not
mistaken) an essential issue in discrete computational mathematics.
Jim Bromer
On Tue, Jun 25, 2019 at 2:09 PM Jim Bromer wrote:
> I think Newton's met
be
used to simplify complicated (and complex) ordering functions.
On Tue, Jun 25, 2019 at 8:20 AM Jim Bromer wrote:
> Brett,
> Steve has been talking about something similar. I understand the value of
> being able to add and subtract rates or ratios as a substitute for
> multiplication
that you have all the answers, it only means that the everyday
mental static of a mind that spends too much time idling no longer
interferes with your ability to think clearly.
Jim Bromer
On Wed, Jun 12, 2019 at 12:03 PM wrote:
> Just imagine how boring it is to do the dishes. programm
in a specialized AI program, just because
the program is specialized and does not need to apply the broad range of
utilizations that conventional mathematics can reach.
I am interested in the video of the Hierarchies and I will watch it tonight.
Jim Bromer
On Tue, Jun 11, 2019 at 10:05 PM Brett N
could design something that was efficient for my specially designed
computational methods. The solution (to that little sub-problem) is to keep
the mathematical abstractions of computation separate from the rest of the
concept data base. It could be kept in RAM using an efficient look up
method.
Jim
I guess that I really don't have any good ideas for a special mathematical
computational system. I want to use strings of types and specifics but they
won't be mathematical and they won't be text. But the idea of keeping
fundamental relations based on learned types separate from the other
.
Jim Bromer
On Thu, Jun 20, 2019 at 1:13 PM Steve Richfield
wrote:
> Jim,
>
> Many systems, e.g. while adding probabilities to compute probabilities
> doesn't make sense; adding counts having poor significance, which can look
> a lot like adding probabilities, can make sense to
.
Jim Bromer
On Thu, Jun 20, 2019 at 7:33 PM Matt Mahoney
wrote:
> I disagree. By what mechanism would neurons representing feet and meters
> connect, but not kilograms and liters?
>
> Neurons form connections by Hebb's rule. Neurons representing words form
> connections when th
I think your use of metaphors, especially metaphors that were intended to
emphasize your thoughts through exaggeration, may have confused me. Would
you explain your last post Steve?
On Thu, Jun 20, 2019, 12:02 PM Steve Richfield
wrote:
> Too much responding without sufficient thought. After a
I guess I understand what you mean.
On Thu, Jun 20, 2019, 12:07 PM Jim Bromer wrote:
> I think your use of metaphors, especially metaphors that were intended to
> emphasize your thoughts through exaggeration, may have confused me. Would
> you explain your last post Steve?
>
>
, 12:08 PM Jim Bromer wrote:
> I guess I understand what you mean.
>
> On Thu, Jun 20, 2019, 12:07 PM Jim Bromer wrote:
>
>> I think your use of metaphors, especially metaphors that were intended to
>> emphasize your thoughts through exaggeration, may have confused me. W
That idea did not work. You can send 1 of 6 states in 2 clock cycles with
the method I was talking about but if you have a no-voltage state then you
can send trinary digits and you can represent 1 of 9 states in 2 clock
cycles.
Jim Bromer
On Sun, Jun 23, 2019 at 1:51 PM Jim Bromer wrote:
>
to be statically represented
using all 3 dimensional bits could the circuit be nested with similar
circuits and used for compressing computations? It is going to take me some
time to figure this out.
Jim Bromer
On Thu, Jun 20, 2019 at 9:54 PM Jim Bromer wrote:
> I guess I should have not s
I think the effective voltage compression in the voltage/timing binary
transmission model would approach 1/3 or 1/4. I cannot remember which one
offhand.
Jim Bromer
On Sun, Jun 23, 2019 at 1:38 PM Jim Bromer wrote:
> I should have said: The method that neurons form generative 'connecti
The 'formal' part of the system can be acquired through learning.
Jim Bromer
On Wed, Jun 12, 2019 at 9:14 PM wrote:
> Yeh Steve - maybe that helps it try novel situations better???
> newsflash from me -> i think that formalizing the system manually ends up
> a shallower system tha
histication.
What I am getting at is that these ideas could be tested in highly
controlled tests. If I was working for a software company I might propose
writing some of these controlled tests in order to better study the kinds
of things that I am talking about.
Jim Bromer
On Wed, Jun 12, 2019 at 9:55 PM
as
a 2-sided sword? I do think I will need to use hierarchies but not in the
sense of a strict traditional logical hierarchy.
Jim Bromer
On Tue, Jun 11, 2019 at 1:59 PM Nanograte Knowledge Technologies <
nano...@live.com> wrote:
> Jim, I think what you're describing here has relevance fo
you have is ideas. Some of those ideas may be insightful but
still...
Jim Bromer
On Sun, May 19, 2019 at 1:20 PM Mike Archbold wrote:
> A crackpot to me is somebody out of touch with reality, such as one having
> delusions of grandeur. Their methods are unsound (I like Apocalypse Now
&
If you included yourself in your response it would be worthy of some
respect.
Jim Bromer
On Sun, May 19, 2019 at 6:13 AM Giacomo Spigler wrote:
> Funny that everybody answering is only showing how the OP was completely
> right.
>
> G
>
> On Sun, May 19, 2019, 10
https://www.sciencedaily.com/releases/2019/07/190703150501.htm
Jim Bromer
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am not arguing about the merits of studying
other ways to create AGI, I am only pointing out that our approach is sound
- except that most of us are not actually conducting experiments.
Jim Bromer
On Thu, Jul 4, 2019 at 7:51 AM Nanograte Knowledge Technologies <
nano...@live.com>
es sense even if it
is not how neurons work.
Jim Bromer
On Thu, Jun 20, 2019 at 12:02 PM Steve Richfield
wrote:
> Too much responding without sufficient thought. After a week of thought
> regarding earlier postings on this thread...
>
> Genuine computation involves manipulating
If, in some weird world you weren't using AC current, be careful about
going with amped up current.
Jim Bromer
On Fri, Jun 28, 2019 at 5:43 PM Jim Bromer wrote:
> Did you rectify AC current? That is pretty close to the extent of my
> knowledge about electronics. I once sawed a 2 to
feel
that I can probably make primitive versions of some of the ideas that I
have. While these primitive variations won't work efficiently they still
might turn out to be interesting. Coming up with a great example is
impossible but coming up with something unusual is very possible.
Jim Bromer
the individual features that occur in the data that
contains something that it is trained to detect is why DL is not AGI. It is
not even narrow AGI. It may become narrow AGI but it definitely is not
there yet.
Jim Bromer
On Thu, Aug 8, 2019 at 12:46 PM Brett N Martensen
wrote:
> Jim, You are ri
Perhaps the detection of simple things that are composed of simpler but
more general things is still rooted in metaphysics because we don't have
good models (of how abstraction, composition and so on work) which can
explain it adequately.
Jim Bromer
On Thu, Aug 8, 2019 at 1:06 PM Mike Archbold
son does not pick up on it. (Dig?)
You should not get annoyed with other people when you are tying to explain
cool. On the other hand, the Phonz did show some flashes of annyance when
Potsie or one of the other characters was being a little square. But keep
your uncool brief dude. That's you, not your squar
for you to understand in a few
minutes of reading? The conference is just about to start. Is it really
worth your time to think about what I am trying to say? Right now it is not
worth your time to respond. In a few years it will probably be very
relevant to what you would like to do.
Jim Bromer
On
Unfortunately AGI looks like it will oneday be a great surveilance tool.
I am going to have to borrow that Kerouac quote from you.
Jim Bromer
On Sat, Jul 27, 2019 at 11:59 AM Ben Goertzel wrote:
>
> http://anewdomain.net/ben-goertzel-whats-so-disturbing-about-microsofts-openai-inve
it is
just a crude simulation? By being developed along the way.
Jim Bromer
On Thu, Aug 8, 2019 at 10:45 AM Steve Richfield
wrote:
> Jim,
>
> Here is a video that illustrates my wake-up call regarding real-world
> complexity:
>
> https://www.youtube.com/watch?v=fVet82IUAqQ=369s
to show that the same can be done with other 'fields'. The only issue is
that everything would have to be kept at an extremely simple level and that
'genuine learning' is actually taking place. Defining and developing
general learning is the only problem other than complexity.
Jim Bromer
al process definition can't be rocking and rolling without being
grounded.
But the real question is: Would this have anything to do with AI and AGI? I
think it must. I mean, if it can be defined then it probably will have some
effect on AI and AGI. But I don't know for sure.
I wasn't going to spend much time on this but the problem may be more subtle
than you seem to appreciate. The solution for one or two points on a curve
contains less information than the equation of the curve. And that made me
realize that a curve or even a straight line has an infinite number
What's this got to do with AGI? Maybe nothing.
https://www.nytimes.com/2020/02/05/science/quadratic-equations-algebra.html
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I have not been able to come up with a way to overcome p!=np
in logic, so I am thinking about developing a heavily typed logic (logic-like
references) as a way to get around the bottleneck of exponential complexity.
However, I have run into some difficulties there as well.
I would like an object
Being able to solve a quadratic equation with a linear solution is a kind of
compression and it is a compressed operation (on the data) which is also
important. I have not be able to show that it is a general solution (for
parabolas that have been rotated for example) but I think that it might
That is typical of exaggeration. You can often get things for free. Therefor
your criticism is not therefore because you did not actually test your
critical theory out in any way.
I am unable to see how this solution, or the other surprising relations the
conic sections have to a broad
Therefore you criticism is not relevant because you did not actually...
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For instance, I can create a simple logical formula for any three variable
statement without using any of the variables in more than one sub formula.
However, I have to introduce a new kind of operation. I can probably do the
same for any 4 variable statement and so on, but the question is
The given solution to the parabola is a solution of the intersection of a
straight line and the parabola. Is it possible that there is a solution to the
intersection of a cubic equation and a quadratic equation that could be solved
by solving for a quadratic equation? If the 'trick' can be
If you flipped a coin and it came up heads then the probability that it came up
heads is 1.
Was that a trick question?
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Wow I did not even see this discussion before I wrote my comments about free
stuff in another thread. I do not remember (and do not care right now) where
the no free lunch concept started. But I see it as there is a cost somewhere.
But there ca*n always be efficiencies that have not been
A mathematical model of telepathic intuition?
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I do not want to parse everything imortal.discoveries said, but my feeling is
that as an AI program learns more, it will need to keep relatively more
specialized data and it will need to create more 'indexes' (or something that
acts like an index) into the data. So it will create an
So I guess my point of view would be that mathematics, in the contemporary
common sense of the term, is not adequate for AGI. I do not think that human
beings have ultimate compression-decompression systems that are responsible for
thinking although some kind of effective compression
I think we have to explore in order to learn - and in order to utilize our
knowledge. But it is nicer when we can do so wisely. So we explore areas that
we do not know well in order to expand our knowledge which includes the
application of knowledge that we have already acquired. But when we
If there was no such thing as a free lunch all progress would have been
impossible. By falling into your presumptions you lock yourself into them.
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It sounds like you are predicting that you will be unable to make any progress
(in the versions of) ML (that you have in mind).
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A 'free lunch' is possible because human beings do not know everything. That
means that new efficiencies can be discovered. Even though you may discuss a
frame work as if it were the only basis to achieve a goal the argument does not
prove the premise that the particular frame work you have in
That is a very interesting point, but in talking about a uniform probability
distribution over an infinite set you are characterizing the issue as if it
were the universal characterization that underlies any characterization (of all
possible universal generalizations).
Since you expend calories on things other than getting more calories then that
implies that every lunch that is sufficient to sustain you must be partially
free. You get more calories from lunch then you expend getting it. Suppose that
there was some supremely efficient characterization of a
And it is relevant to the task and equipment that can be used on the task.
My point is that there may be issues, like compression, that may be designed
specifically for AI or AGI which may work better than more general compression
methods. But that also means that they may not be as effective
If there was no such thing as a free lunch then we would all be living in the
stone age. Every advancement is based on some kind of efficiency. Yes, those
achievements come at a cost. So there may be a relative trade-off but the loss
of generality from a purely imaginary (unattainable ultimate
Danko,
I think your comment is closer to a reasonable definition but I am not sure
that is the common definition. The no free lunch idea is a very useful bit of
insight but treating a rule that does not typically transcend the premises of
its application as if it could is a mistake or at least
I am learning a little. The no free lunch theorem depends on the analysis of an
imperfect system that will lead to perfect knowledge. But in real world it is
possible that someone might come up with a solution to a complicated problem
that would have to be heavily developed in order to be
I was thinking about it and the No Free Lunch theory is relevant to a large
number of computational algorithms, but it is not a problem when the time
differences (between runs of an algorithm) do not bother us. By thinking about
simpler problems I was able to start to see some of the related
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