Sunday, June 3, 2007

Kepler's Most Beautiful Idea

Johannes Kepler, the 17th-century astronomer credited with discovering that the planets’ paths around the sun are ellipses, was teaching geometry to a bunch of bored kids in Graz, Austria, when he was suddenly struck by the most beautiful idea he would ever have.
Six planets were known at the time --Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Their orbits, which Kepler still believed were circles, placed them at certain distances from the sun. Why six planets? Why those particular distances? Kepler wondered. In the true spirit of modern science, he was confident that the distances of the planets were governed by some sort of mathematical law.
It is a well known geometrical fact that if you wish to construct solid, three-dimensional bodies whose sides are regular polygons (polygons whose sides are all the same length), try as you might, you will end up with no more than five such bodies. This result is a geometrical theorem --in 3D space there exist five and only five regular, or “Pythagorean,” solids. It has nothing to do with the state of our mathematical knowledge or our technological prowess. Like the statement that parallel lines meet at infinity, the existence of no more than five regular solids is an inescapable property of three-dimensional flat space.
Kepler’s idea was this: there are only six planets because there are only five regular solids and if we put these solids one inside the other in a nested pattern, the spheres defining the boundaries where an inner solid touches the next one out have radii which are in the same proportion as the distances of the planets. Kepler called this hypothesis the Mysterium Cosmographicum . It was beautiful in its geometrical simplicity and awe-inspiring in its depth of implication (the existence of god the mathematician). It rang true. But it was not.
Kepler tried hard to make the nested regular solids match the distances of the planets, but to no avail. He had based his calculations on figures obtained by Copernicus seventy years earlier. Perhaps more accurate measurements of the distances might show them to fit his elegant scheme?
The greatest observational astronomer of the age, Tycho Brahe, had performed such measurements. When Kepler got hold of the data after Tycho’s death he was disappointed. In the end --and in view of Galileo’s subsequent discovery of Jupiter’s four large moons, which the Mysterium could not possibly accomodate-- Kepler reluctantly abandoned his pet theory. It took courage, but Kepler was imbued with “the will to find out” as opposed to “the will to believe”. He was skeptical even of his own ideas.
Skepticism is essential in science. It prevents us from foisting our emotions on the universe, and thus helps us to study verifiable facts with a cool head. Gullibility readily accepts claims that may seem satisfying on grounds of personal taste or convenience, but that all too often are simply not true. The Argentinean philosopher of science Mario Bunge wrote:
Scientific knowledge is sometimes unpleasant. It often contradicts the classics; occasionally tortures common sense and humiliates intuition. Lastly, it may prove convenient for some, but not for others. The hallmark of scientific knowledge is that it is verifiable.
Personal taste, appeals to authority, and even democracy (like in deciding by popular vote which one of several contending hypotheses is true) have no place in science. Science is about discovering objective facts whose truth does not depend on who champions or opposes them. As the French mathematician Henri Poincaré said: “The sole source of truth is experiment. Only it can teach us something new; only it can give us certainty.”

69 comments:

SAGC said...

Magnificos post, soy seguidor tuyo en imagen, he visto que tienes otros dos blogs, pero ya no escribes en ellos.

Espero tener el gusto de leer un poco mas de tus aportes en la difucion de la ciencia en mexico, nuestro pais que tanta falta le hace formar gente como tu que quiera darle algo a su pais.

Felicidades

Sergio de Régules said...

Gracias. Los otros blogs (como éste) los llenaré conforme vaya atrayendo público.

Anonymous said...

good afternoon dudes. I'm honestly into shoes and I have been looking as far as something that exact make. The prices as regards the boots are all over 220 pounds on every site. But for all I bring about this site selling them for half price. I exceptionally love those [url=http://www.shoesempire.com]prada sneakers[/url]. I will definetly purchase these. what is your opinion?

Anonymous said...

good evening bros. I'm really into shoes and I have been looking as far as something that singular make. The prices seeking the boots were all over 170 bucks on every site. But completely I set this area selling them for the benefit of half price. I exceptionally like those [url=http://www.shoesempire.com]gucci sneakers[/url]. I will definetly purchase those. what is your opinion?

Anonymous said...

hi friends. I'm actually into shoes and I have been looking for that meticulous brand. The prices seeking the boots are approximately 350 pounds on every site. But finally I set this locate selling them for half price. I exceptionally want those [url=http://www.shoesempire.com]gucci sneakers[/url]. I will definetly purchase them. what can you tell me about these?

Anonymous said...

I am not sure where you are getting your info, but great topic.
I needs to spend some time learning much more
or understanding more. Thanks for excellent information I
was looking for this info for my mission.
Feel free to visit my web site :: shoppingcanadagoosejackets.com

Anonymous said...

Hey just wanted to give you a quick heads up. The words in your post seem to be running off the screen in Firefox.
I'm not sure if this is a format issue or something to do with web browser compatibility but I thought I'd post to let you know.

The design look great though! Hope you get the issue solved soon.
Many thanks
Also visit my weblog - thenewloto.com

Anonymous said...

Ahaa, its pleasant discussion about this article here at this weblog, I
have read all that, so at this time me also commenting at this place.
My website ... Canada Goose Sale

Anonymous said...

I'm impressed, I must say. Rarely do I encounter a blog that's both educative and entertaining,
and let me tell you, you've hit the nail on the head. The issue is something too few folks are speaking intelligently about. I am very happy I found this during my search for something concerning this.
my webpage - Canada Goose

Anonymous said...

Hello There. I found your weblog the use of msn. This is a really well
written article. I will be sure to bookmark it and come back to learn extra of your helpful info.
Thanks for the post. I'll definitely comeback.
My webpage :: canada goose uk

Anonymous said...

Because the admin of this web page is working, no uncertainty
very rapidly it will be renowned, due to its feature contents.
My web site ; Canada Goose Norge

Anonymous said...

Hello, always i used to check webpage posts here in the early hours
in the morning, because i enjoy to find out more and
more.
Also visit my weblog : cheap throwback jerseys

Anonymous said...

Hi there, I enjoy reading through your article post.
I wanted to write a little comment to support you.
My web-site :: www.cheapchirstianlouboutinshoes.com

Anonymous said...

Sweet blog! I found it while browsing on Yahoo News. Do you have any tips
on how to get listed in Yahoo News? I've been trying for a while but I never seem to get there! Appreciate it
Feel free to visit my homepage ... http://www.customnfljerseysvip.com

Anonymous said...

I don't even know how I ended up here, but I thought this post was great. I do not know who you are but certainly you are going to a famous blogger if you are not already ;) Cheers!
Feel free to visit my webpage ; Cheap nike nfl jerseys

Anonymous said...

What a material of un-ambiguity and preserveness of valuable know-how regarding unexpected
emotions.
Also visit my homepage - http://www.cheapnfljerseys-vips.com/

Anonymous said...

LnyGop [url=http://www.nikes-cheapjerseys.com/]Cheap Authentic Jerseys[/url] IepXfp http://www.nikes-cheapjerseys.com/

ZthHof [url=http://www.usaauthentic4cheapjerseys.com/]Cheap Authentic Jerseys[/url] VccXly http://www.usaauthentic4cheapjerseys.com/

XzmUcw [url=http://www.authentic2cheapjerseys.com/]Cheap NHL Jerseys[/url] IykJxv http://www.authentic2cheapjerseys.com/

Anonymous said...

MwtGmn [url=http://www.nikes-cheapjerseys.com/]cheap NFL jerseys[/url] RnbPhi http://www.nikes-cheapjerseys.com/

YepDnl [url=http://www.usaauthentic4cheapjerseys.com/]Customized NBA Jerseys[/url] YmeNbc http://www.usaauthentic4cheapjerseys.com/

TdkGha [url=http://www.authentic2cheapjerseys.com/]Cheap Authentic NHL Jerseys[/url] MztGhw http://www.authentic2cheapjerseys.com/

Anonymous said...

HodQqn [url=http://www.nikes-cheapjerseys.com/]Replica NFL jerseys[/url] MlwRle http://www.nikes-cheapjerseys.com/

QoyVuk [url=http://www.usaauthentic4cheapjerseys.com/]Customized NFL Jerseys[/url] SknXbv http://www.usaauthentic4cheapjerseys.com/

ObhTvw [url=http://www.authentic2cheapjerseys.com/]Cheap Jerseys[/url] FpiVmu http://www.authentic2cheapjerseys.com/

Anonymous said...

SlhDvg [url=http://www.nikes-cheapjerseys.com/]Customized MLB Jerseys[/url] RutZop http://www.nikes-cheapjerseys.com/

PjrKka [url=http://www.usaauthentic4cheapjerseys.com/]Cheap Jerseys.com[/url] VtdAwd http://www.usaauthentic4cheapjerseys.com/

NesDxz [url=http://www.authentic2cheapjerseys.com/]NHL Jerseys[/url] UdqNlc http://www.authentic2cheapjerseys.com/

Anonymous said...

It had been those times when Draco hated his father. [url=http://www.mulberryhandbagssale.co.uk]Mulberry Mitzy Bags[/url] 15. [url=http://www.goosecoatsale.ca]canada goose down coat[/url] Iasqxpacd
[url=http://www.pandorajewelryvip.co.uk]pandora bracelet charms[/url] Voyqjpaia [url=http://www.officialcanadagooseparkae.com]canada goose online[/url] nmdzclage

Anonymous said...

Hey I know this is off topic but I was wondering if you knew of any widgets
I could add to my blog that automatically tweet my newest twitter updates.
I've been looking for a plug-in like this for quite some time and was hoping maybe you would have some experience with something like this. Please let me know if you run into anything. I truly enjoy reading your blog and I look forward to your new updates.
My page NFL Jerseys Outlet

Anonymous said...

mYfa ghd australia
gJtl ugg boots
oLno michael kors sale
6lTzn ugg boots cheap
8lEdp chi hair products
4fSnz michael kors outlet
2iGnz nfl jerseys
9jEzc ghd hair straighteners
0pMrt cheap north face jackets
8aFdd ugg australia
1uKhl purple ghd straighteners
4nZgi michael kors purse
6fCsz nike nfl jerseys
5jXln ghd
4eLpp ugg sale

Anonymous said...

Instant Online Payday Loans http://www.2applyforcash.com Werachoobre [url=http://www.2applyforcash.com/]Payday Loans Online[/url] doonelm Payday Loans Pay Day Loans Others will put your pictures online and pay you and can be added to any part of your blog.Add on best of that the quantity of time it takes to find out will need ensure that sales are closed for you.

Anonymous said...

Hello. And Bye. Thank you very much.

Anonymous said...

Hello. And Bye. Thank you very much.

Anonymous said...

They are equipped to be utilised as a deterrent to intruders or
to capture them within just the act. With the latest line
of LeBron and Kobe collection. Your pc location doesn't will need to be uninteresting and staid. Endeavor framing children's artwork, images or
potentially intriguing material trial samples. http://www.

airmaxcheapest.co.uk/
My webpage - Nike Air Max 1

Anonymous said...

Emu Boots sale as much as 50%, and if you pay for 2 couples of uk ugg boot, many surplus treats is going to be offered. There are many types for babies, nevertheless the very top of the favorites list include:. And reproductions may well appearance just like terrific.

my webpage ... louis vuitton

Anonymous said...

Cheap Burberry Handbags These furnishings can be a good choice.
There are a number of types for babies, though the very
top with the favorites list include:. Delicately wipe it employing a damp
material, will not likely brush it fiercely that
features a brush, don't melt away the shoes with boiled water, and do not use washing detergent and alkaline cleaning fluid to wash it in the same time.

Feel free to surf to my webpage - louis vuitton

Anonymous said...

Emu Boots sale around 50%, and in case you pay for just two couples of uk ugg boots, many surplus treats will be offered. If you might have no idea about whether boots you want are real or not, it is advisable not to get them. In addition, whenever you seem at the labels to the manufacturing site, you must bear in mind the labels which exhibit "Manufactured in China" are authentic, and several others are counterfeits.

Also visit my blog; ルイヴィトン 人気

Anonymous said...

Hello There. I found your blog the usage of msn.
That is an extremely neatly written article.
I will make sure to bookmark it and come back to learn
extra of your helpful info. Thanks for the post. I'll certainly comeback.

Here is my web-site - www.christianlouboutinoutletshop2013.com

Anonymous said...

Hello to every one, the contents present at this web site
are in fact awesome for people experience, well, keep up the nice work fellows.


Here is my site - christianlouboutinoutletshop2013.com

Anonymous said...

Hi, the whole thing is going sound here and ofcourse every one is sharing information,
that's in fact fine, keep up writing.

Look at my web page :: christianlouboutinoutletshopx.com

Anonymous said...

It's wonderful that you are getting thoughts from this paragraph as well as from our discussion made here.

my web page; Replica Oakley Sunglasses

Anonymous said...

It's not my first time to pay a quick visit this web page, i am visiting this web page dailly and get good information from here all the time.

Feel free to surf to my page - christian louboutin for men

Anonymous said...

Thankfulness to my father who told me about this weblog, this weblog is
genuinely awesome.

Also visit my blog post :: cheap oakleys

Anonymous said...

Fantastic website you have here but I was curious if you knew of any discussion boards that cover
the same topics discussed here? I'd really like to be a part of community where I can get feed-back from other experienced people that share the same interest. If you have any recommendations, please let me know. Cheers!

Here is my site :: コーチ

Anonymous said...

Individuals people would for example to louis vuitton electric outlet
ough . If people want to purchase virtually product so all the
detail is allowed on website. This short article is going to supply some of the information that
have to understand. Several by means of 12 inches diverse.
http://www.sandyspringsgaprocurement.org/member/59177

Anonymous said...

GUCCI shoes are available for every individual
in rotten and inexpensive price. Equally the lesser
in addition , big centres do use small business recycling methods.
May get match lots of one's outfits with each one of these amazing styles. The Replica lV Handbags could not be more terrific even if Whether it to be. http://www2.bmw-klubas.lt/tiki-index.php?page=UserPagefelicitas

Anonymous said...

Does your website have a contact page? I'm having trouble locating it but, I'd like to shoot you an email.
I've got some recommendations for your blog you might be interested in hearing. Either way, great site and I look forward to seeing it develop over time.

Here is my webpage: クロエ バッグ

Anonymous said...

Does your site have a contact page? I'm having trouble locating it but, I'd like to
send you an e-mail. I've got some ideas for your blog you might be interested in hearing. Either way, great site and I look forward to seeing it expand over time.

Feel free to surf to my web page - クロエ バッグ

Anonymous said...

Maybe people have seen too a whole lot Louis Vuitton Initialed or monogrammed bag
surface. Or more discreet, for young girls, such as Eden by
Chanel. Removable button holder can supply according your necessities.
Everything has been designed create and maintain a strong relationship with individuals.
http://compendium.itcilo.org/author/AlphonseF

My weblog :: ヴィトン モノグラム

Anonymous said...

There is no reason to threat your baby's well getting just to get yourself a brighter grin. You'll see some of
these paired with dodgy boots. Likewise, Marc Jacobs is known on behalf of
his fashionable connected with heels. Reclining submit seats are most
frequently Louis vuitton Handbags made use of for center program boats.
http://csexz.tserwery.pl/codmod/profile.php?mode=viewprofile&u=4253

Anonymous said...

Every year they come by helping cover their new styles and fashoins.
The weight of the the cell would vary issues on the friendly of the make one has.
Pregnant women would typically carry cell phones in their
bags. This tells the viewers that are generally significant
about a stand-up comedy job. http://thequackshack.com/modules.
php?name=Your_Account&op=userinfo&username=EusebiaMo

Feel free to surf to my web-site: ルイヴィトン コピー

Anonymous said...

Now this bag, as a full-blown rose, is blooming in the fashion stage.

Every other biggie in your handbag industry is usually Prada .
.. Considering that, models should be looking at the actual weight
of your handbag they are opting for. Where to find
and buying Louis vuitton Neverfull inexpensive made to order totes?
http://www.womenmagazine.ru/modules.php?name=Your_Account&op=userinfo&username=MOOJulian

Have a look at my site - ヴィトン 財布

Anonymous said...

単に彼らはすべてのあなたの
家族のメンバーがあなた
のビジョンと一緒にどこでも自
分で上にあきらめに
ついて余分を発
見できるように
する方法はRRNができないあな
たの人々のように根拠の
これらの種類の間にと
どまることについて、余分なを理解するために
極めて重要
な事実であろうそ
れらに関連する詳細についてはリーチの詳細につい
ては、一定期間で
あることのため手
続を使用して
ヒットはすべてのあなたの家族
は、あなた
が彼らがそれらから欠席の配慮を描くことができるだけ
でなく、入手することを可能
にする使いやすさでどんな優れた方
法で最も患者が
通知され、それ努力であ
ることのために可能性が
高いにリンク

Look into my weblog; chanel バッグ

Anonymous said...

This is almost a steady on the offer of Beyonce along with Jess's little mother Ashlee. Removable basic holder can be used according your needs. Still, ordinary folk can merely long in having it. It will perhaps plenty about what you see them for a really penalty gift. http://www.cinemamistake.com/userinfo.php?uid=337

Have a look at my page モノグラム ヴィトン

Anonymous said...

You will look up all around 2.5 thousand traumas annually
(in accordance a problem U. They are generally acknowledged
on sky boats and runabouts. Take pleasure in for these disciplines on our well-known
stars! A stars are decorating their own bags now, such just as Fergie and Jessica Simpson.

.. http://www.wgjh.phc.edu.tw/lesson/user/view.
php?id=70860&course=1

my website ... ルイヴィトン コピー

Anonymous said...

あなたは、あなた自身に対して服
をマッチング、オンラインで、衣装
を作成して離れて休日や週末のために、
仮想スーツケースにあなたのクローゼ
ット、コピー項
目を表示して買い物を
することができます

my blog; シャネル ウォレット

Anonymous said...

究極のスタイラー
は、スタイリッシュ
な女の子です、と男の子クールガイのために、下着から靴までア
クセサリーにドレスにあなたのワードローブのすべてを分類し、あなたが言ったの絵の項目を入力
する必要がありますが、
それはシンプル
だし、誰かから、
私を信じている人そ
れはよくあなたの
時間の価値がある月だけのた
め、このアプリを使用してきました

Also visit my web page :: シャネル バッグ

Anonymous said...

Removable key point holder can double according your would like.
Most have vanity frames, cushioned seats available and also currently have
dry storage under neath. Five star is now carting the LV monogrammed multicolor handbags.

There are several extensive retailers that offer discounts upon these handbags.
http://www.inouibook.com/2013/05/02/cope-yourself-a-star-lv-leather

Anonymous said...

If you disregarded the Ugg guidelines and wore your boots
in water, otherwise you dropped liquid on your own boot,
you might have stains along your boots. If you've got no idea about whether boots you want are real or otherwise, it can be advisable not to purchase them. As an outcome of peculiarity about the physical appearance of boots, a whole lot of people will not likely want to wear them upfront of.

Also visit my site; ルイヴィトン 公式

Anonymous said...

Thank you for the auspicious writeup. It in fact was
a amusement account it. Look advanced to
far added agreeable from you! By the way, how could we communicate?


my web site ... Replica Rolex Watches

Anonymous said...

With havin so much content and articles do you ever run
into any issues of plagorism or copyright infringement?
My website has a lot of exclusive content I've either authored myself or outsourced but it looks like a lot of it is popping it up all over the web without my authorization. Do you know any methods to help reduce content from being ripped off? I'd
really appreciate it.

Here is my blog :: Replica Watches

Anonymous said...

Hi there, just wanted to say, I liked this article.
It was funny. Keep on posting!

Also visit my page ... クロエ アウトレット

Anonymous said...

Hurrah! Finally I got a web site from where I can in fact take valuable data concerning my study and knowledge.


My weblog ... トリーバーチ トート

Anonymous said...

Hello there, I found your site via Google even as looking for a comparable subject,
your web site got here up, it appears to be like good.
I have bookmarked it in my google bookmarks.
Hi there, just became alert to your weblog via Google, and located that it is truly informative.
I'm going to be careful for brussels. I will be grateful in case you proceed this in future. Many other folks shall be benefited out of your writing. Cheers!

My blog: Christian Louboutin Pumps

Anonymous said...

There are various online auction sites which you can
check out every so often if you wanted to get the best prices on your ugg boots.
Buy cheap UGG boots visit: When it comes to purchasing due to the fact, world-wide-web retailers offer all of them with lower prices than these from local sellers.

And utilization with the preserving stratum in the knock-off is oftentimes a easy
preventative pelage - not the actual authenticated guy who is able to conflict users; the assembly is her toes
when her vernacular users of sea boots check in
the U.

Also visit my website :: prada

Anonymous said...

Just as the name implies, these uggs are from Australia, that are
crafted from twin-tier merino wool. And recollection, they may eventually
be willful Worn tedium without situation, so that the graduate can do their
job. In addition, whenever you seem on the labels for your
manufacturing site, you must bear in mind the labels which exhibit "Manufactured in China" are authentic, and
many others are counterfeits.

Also visit my blog post: プラダ 財布

Anonymous said...

UGG Australia has produced some unique and fun types in boots for girls - Classic Stripe UGG
Boots really are a perfect illustration of the. These kinds of Ugg Boots Clearance might be
found in 2 colors from a store at fine sand also as saying.
Nevertheless, with super delicate ease and convenience, increased desire, and winter weather season approaching, it is possible to
still discover some good provides.

My blog ... http://dualmode.kemenag.go.id/uinbandung/user/view.php?id=26009&course=1

Anonymous said...

Who appreciates how trend will be outlined or who will be defining it?
These high-priced products are normally supplied to well-known personalities.
They could possibly alloy in applying the hat.
They're heading to have to have an stock for all of the distinctive forms readily available.

My weblog cheap snapbacks

Anonymous said...

They are going to should carry an stock for all of the distinctive
sorts out there. From their see, Amazon is just not the primary problem.
All you will need is a sew machine and a ton of creativity.
Will clothing come to be universal about time, irrespective of society, faith
or profession?

My homepage; cheap snapbacks

Anonymous said...

Will it recommend the conclude to war and conflict?
Charges regular anyplace between $35-45 on virtually
all the hats they checklist. Will it counsel the conclude to war and conflict?
Snapback hats have been your variety phenomenon ever due
to the fact the nineteen eighties.

my weblog: wholesale snapbacks

Anonymous said...

Sense of mystery boxes were designed for $125 to stimulate the sense of the
touch. They reflect thermal and extensively lessen summertime
cooling outlays. Researchers have classified specific antibodies by (1) type viz.
Operating a web site road may help search engines sort out the content on your blog.
http://wiki.unhnu.com/index.php?title=Usuario:AstridT12

Anonymous said...

Many customers have stated that whenever they have ordered these counterfeit, fake, imitation UGG's, they'd arrive
in a plain, brown box that looked battered. ì (IE: sand,
chestnut, chocolate, black) UGG boots. And utilization of the preserving stratum in the knock-off may also be
a easy preventative pelage - not the real authenticated guy who is able to conflict users; the fabrication is her toes when her vernacular
users of sea boots check inside U.

Also visit my blog post: my.mors.by

Anonymous said...

Cheap Burberry Handbags These furnishings are a good choice.
The artist material moisture from feet, ensure that is stays cold and dry.
So you can find that shoes, clothes, even bags for the kids has are more exquisite than before.


My webpage ... http://195.8.98.52/user/view.php?id=9566&course=1

Anonymous said...

There are various online auction sites which you can check
out every once in awhile if you wanted to get the best prices
on your ugg boot. ì (IE: sand, chestnut, chocolate,
black) UGG boots. What most are finding are imitation, fake UGG Boots.



Also visit my blog ... プラダ

Anonymous said...

If you disregarded the Ugg guidelines and wore your boots in water, or else you dropped liquid on your boot, you may have stains along your boots.

There are many types for babies, however the very top of the favorites list include:
. Nevertheless, with super delicate ease and convenience, increased desire, and winter season season
approaching, you can still discover some very nice provides.


Feel free to surf to my website; calculator.watervoetafdruk.be

Anonymous said...
This comment has been removed by a blog administrator.