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Mathematicians Devise Typefaces Based On Problems of Computational Geometry

Soulskill posted about 6 months ago | from the extending-comic-sans-into-all-dimensions dept.

Science 60

KentuckyFC writes: "Typeface design is something of an art. For many centuries, this art has been constrained by the materials available to typographers, mainly lead and wood. More recently, typographers have been freed from this constraint with the advent of digital typesetting and the number of typefaces has mushroomed. Verdana, for example, is designed specifically for computer screens. Now a father and son team of mathematicians have devised a number of typefaces based on problems they have studied in computational geometry. For example, one typeface is inspired by the folds and valleys generated by computational origami designs. Another is based on the open problem of 'whether every disjoint set of unit disks (gears or wheels) in the plane can be visited by a single taut non-self-intersecting conveyor belt.' Interestingly, several of the new typefaces also serve as puzzles in which messages are the solutions."

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I think i will stick with Times New Roman... (1)

SlickUSA (1749194) | about 6 months ago | (#46786969)

...before having to decipher those dots and lines

Re:I think i will stick with Times New Roman... (2)

i kan reed (749298) | about 6 months ago | (#46786991)

You didn't actually see the font, the first image was just about analyzing character structure in a mathematically objective way.

Re:I think i will stick with Times New Roman... (1)

Anonymous Coward | about 6 months ago | (#46787453)

There is no "the font", the paper contains a number of fonts, one of which was the first image in the article. RTFA before telling people to RTFA, sheesh!

Re:I think i will stick with Times New Roman... (1)

i kan reed (749298) | about 6 months ago | (#46787525)

I didn't. RTFP.

Re:I think i will stick with Times New Roman... (0)

Anonymous Coward | about 6 months ago | (#46788281)

The paper contains typefaces described by a font.

Question answered (5, Insightful)

bws111 (1216812) | about 6 months ago | (#46786977)

Well, at least now we know why typefaces are designed by artists and not mathematicians.

Re:Question answered (3, Insightful)

K. S. Kyosuke (729550) | about 6 months ago | (#46787011)

I don't know, Computer Modern didn't turn out all that wrong.

Re:Question answered (4, Insightful)

bws111 (1216812) | about 6 months ago | (#46787053)

True, but I would say that was created by Knuth in the role of artist, not mathematician.

At least ... (3, Funny)

Anonymous Coward | about 6 months ago | (#46787161)

Well, at least now we know why typefaces are designed by artists and not mathematicians.

Next thing you know we're going to have software engineers designing user interfaces and wording menus ... oh wait.

Useless bullshit (0)

Anonymous Coward | about 6 months ago | (#46786981)

Hope this wasn't done in time paid for by any grant money.

This is of no use to anyone.

And I love mathematics pretty much more than anything.

Re:Useless bullshit (1)

Travis Mansbridge (830557) | about 6 months ago | (#46787217)

What if you need to jot something down and all you have is some glass, a furnace, some aligning pegs...

Re:Useless bullshit (4, Insightful)

matria (157464) | about 6 months ago | (#46787233)

Oh really? I would find such a thing extremely useful in creating knitting and other needlework designs. There is a fairly standard set of images for creating pattern charts, but a font representing these stitches would be even better - no need for the usually Windows-only pattern creation software that uses these standardized images.

Re:Useless bullshit (1)

matria (157464) | about 6 months ago | (#46787285)

Well. This got me curious, so I did some research and found that there are, indeed, such fonts. Thank you for your attitude. If you hadn't felt that such a thing was useless because you didn't happen to see a use for it yourself, I wouldn't have been irritated enough to go looking. You see, that was the reason why my father, then my husband, kept me from ever getting my hands on a computer until he decided he could use one after all.

Re:Useless bullshit (2)

Matheus (586080) | about 6 months ago | (#46788023)

Commas are such dangerous weapons... All of the deep seeded psychological issues exposed aside, the incest described by your final sentence would be cleanly done away with by removing most of the commas utilized. You could alternatively replace the word 'then' with 2 words 'followed by' or even easier 'and then' to make your intentions clear.

I may stand corrected in which case I owe your Husband-Father an apology (and child protective services a phone call!)

Re:Useless bullshit (0)

Anonymous Coward | about 6 months ago | (#46788145)

How do panda's party?

Eats shoots and leaves OR
Eats, shoots and leaves

Old joke (1)

ZeroPly (881915) | about 6 months ago | (#46790611)

A mathematician decides he wants to learn more about practical problems. He sees a seminar with a nice title: "The Theory of Gears." So he goes. The speaker stands up and begins, "The theory of gears with a real number of teeth is well known ..."

Who's paying for this shit? (0)

Anonymous Coward | about 6 months ago | (#46786985)

Time for these guys to work in the real world, instead of playing with paint all day.

missing the point? (4, Insightful)

tverbeek (457094) | about 6 months ago | (#46786997)

Traditionally, typeface designers have considered legibility and aesthetics in their work (in addition to typesetting limitations). Apparently those factors are optional now as well.

OK, these are interesting intellectual exercises. But don't try to sell them as examples of typeface design, because that's a creative discipline that goes beyond mathematical questions of "can it be done?"

Re:missing the point? (0)

Anonymous Coward | about 6 months ago | (#46787033)

Yes, you definitely are missing the point. At least you asked though.

Re:missing the point? (3, Insightful)

i kan reed (749298) | about 6 months ago | (#46787039)

Yes, every characteristic is optional. e.g. comic sans and windings. Attempting an objective solution to an artistic problem isn't bad, the complaints that come out of that can help point you towards better objective constraints. Assuming you've succeeded because you're trying to be objective would be the only problem.

Re:missing the point? (4, Funny)

Anonymous Coward | about 6 months ago | (#46787047)

Traditionally, typeface designers have considered legibility and aesthetics in their work (in addition to typesetting limitations). Apparently those factors are optional now as well.

Since context, meaning, grammar, and style all seem to be actively discouraged in modern communication, why not use an illegible font as well?

Re:missing the point? (3, Informative)

celebril (3620861) | about 6 months ago | (#46787475)

The funny thing is that this sort of mathematical and reductionist take on font "design" is precisely what modernism and then postmodernism did to other art forms — by stripping a tradition of its presupposed axioms, picking a certain point as a "first principle", establishing an alternative deriviation from it, and then calling that "art". I hope the typographers hold out, unlike what has become of fields such as sociology, post-tonal music, and continental philosophy.

Re:Re:missing the point? (0)

Anonymous Coward | about 6 months ago | (#46789423)

Agreed. Nothing enrages me more than massive amount of faux-philosophers that took Husserl's ideas and objectives (or the Heideggerian mess that followed), remixed them with some freudian/marxist/antiscientist blabber and ended up being read way more by most of my dear european colleges (yes there are one or two that have a book that is worth a read). Also don't get me started on the rising bunch of "we can't get a sentence straight" analytic philosophy researchers.

Re:missing the point? (1)

AthanasiusKircher (1333179) | about 6 months ago | (#46790665)

The funny thing is that this sort of mathematical and reductionist take on font "design" is precisely what modernism and then postmodernism did to other art forms â" by stripping a tradition of its presupposed axioms, picking a certain point as a "first principle", establishing an alternative deriviation from it, and then calling that "art".

Umm, I don't think you know what postmodernism [wikipedia.org] is. You're actually describing something closer to "modernism" in most art forms, which was generally about rejecting traditional aesthetic criteria and founding new systems. Postmodernism, as a broad artistic idea, is largely a reaction against these "modernist" systems, often drawing on older, more traditional techniques and styles, perhaps in novel or eclectic ways.

For example, you include "post-tonal music" as your only representative art form, but many postmodernist composers (or at least composers who would be identified as such) actually tend to write tonal music of various sorts. It may not always sound like Bach or Beethoven, but it's more likely to connect with older traditions or to develop older tonal systems than the complete break with the past that is often associated with "modernist" music.

As for sociology and continental philosophy -- well, one could argue that continental philosophy has turned all humanities departments into sociologists, rather than literature scholars or historians or whatever. It's true that "postmodernism" as an academic and philosophical idea may seem a bit different, but it was essentially about tearing down the novel systematizing impulses from the early 1900s in areas like logic and epistemology in a similar fashion to what artists did in questioning these systems in the arts.

The apparent conflict is that a lot of scientists and philosophers actually still find the systems of the early 1900s to be useful in those fields, so postmodernism there seems to be a rejection of the "useful" strands of modernism. But in the arts, the "modernist" systems were and often still are a harder sell for aesthetic appreciation... so "postmodern" art, architecture, and music is actually much more palatable to most audiences.

Re:missing the point? (0)

Anonymous Coward | about 6 months ago | (#46787589)

The fact that letters and numbers are being used is incidental. They could be modeling constellations - but letters are the most recognizable shape (at least in parts of the world that uses this alphabet).
None of these "fonts" are intended for use. Rather, the alphabet provides a useful set of 26 shapes upon which these geometric techniques / problems can be modeled. The alphabet is being used as a set of "testing data," nothing more, and provides an interesting and relatable look at various problems in geometry.
However, the fact that this testing data can also be used for communications makes already-interesting demonstration of areas of inquiries in mathematics a little more interesting, particularly for the ones where this is a "puzzle font" form. But that's really a secondary feature.

only one version of the truth (0)

Anonymous Coward | about 6 months ago | (#46786999)

does not require excessive verbiage or phony digitry. digits have 0 physical value ever

Re:only one version of the truth (4, Funny)

SpankiMonki (3493987) | about 6 months ago | (#46787117)

digits have 0 physical value ever

Dunno about you, but my digits come in pretty handy.

you are right (0)

Anonymous Coward | about 6 months ago | (#46787291)

that's pretty funny

Re:only one version of the truth (5, Funny)

cusco (717999) | about 6 months ago | (#46787781)

Considering your username, I think probably even handier than for most people . . .

Interesting... but nearly useless (3, Insightful)

Captain Sarcastic (109765) | about 6 months ago | (#46787013)

The major point of fonts is to improve communications. Clarity and lack of ambiguity are pretty much the main goals we are striving for, with style being important but not vital. These two decided to have some fun with what could be done, and they succeeded. Good for them. Unfortunately, in achieving the style, they failed on the clarity. Time to turn the page.

Re:Interesting... but nearly useless (3, Interesting)

Anonymous Coward | about 6 months ago | (#46787571)

You misunderstand the point of the exercise entirely. None of these fonts are intended for use. Rather, the alphabet provides a useful set of 26 shapes upon which these geometric techniques / problems can be modeled. The alphabet is being used as a set of "testing data," nothing more, and provides an interesting and relatable look at various problems in geometry.
However, the fact that this testing data can also be used for communications makes already-interesting demonstration of areas of inquiries in mathematics a little more interesting, particularly for the ones where this is a "puzzle font" form. But that's really a secondary feature.
The fact that letters and numbers are being used is incidental. They could be modeling constellations - but letters are the most recognizable shape (at least in parts of the world that uses this alphabet).

OK, my mistake. (1)

Captain Sarcastic (109765) | about 6 months ago | (#46787817)

You raise a valid point. I was so intent on the font aspect that I didn't see your take on it. Thanks! (sig line notwithstanding - this is an irony-free post.)

What a waste of time and resources (0)

Anonymous Coward | about 6 months ago | (#46787051)

MIT... why are your students wasting their time and your resources on this? It doesn't solve any problems, nor is it particularly interesting.

-- a confused MIT math alumnus

Re:What a waste of time and resources (1)

retchdog (1319261) | about 6 months ago | (#46787683)

Martin and Erik Demaine are professors, not students.

Erik Demaine, in particular, is widely considered to be a genius [wikipedia.org] , so perhaps it's fortunate that you have no administrative power over your alma mater.

Re:What a waste of time and resources (0)

sexconker (1179573) | about 6 months ago | (#46788111)

Martin and Erik Demaine are professors, not students.

Erik Demaine, in particular, is widely considered to be a genius [wikipedia.org] , so perhaps it's fortunate that you have no administrative power over your alma mater.

Being professors just makes a much worse waste of time and money.
Oh, he's a "genius", is he? Good for him.

Re:What a waste of time and resources (1)

retchdog (1319261) | about 6 months ago | (#46788681)

I'm sure MIT would be thrilled to hear your opinions; they're really floundering and could use all the help they can get. Email them, they've hired people of your caliber [usatoday.com] before.

Idiot.

Re:What a waste of time and resources (1)

sexconker (1179573) | about 6 months ago | (#46790769)

No thanks - I already have a position in academia. I can tell you with complete certainty academia is the epitome of waste and self-congratulatory bullshit.

Spoiler: The fonts look awful! (0)

Anonymous Coward | about 6 months ago | (#46787081)

And our next font is inspired by the intricate designs of Rube Goldberg machines.

Re:Spoiler: The fonts look awful! (2)

graphius (907855) | about 6 months ago | (#46787283)

that I would like to see... PS. for all the naysayers here, There are MANY fonts that approach illegibility and are used for style only. I once worked in a sign shop and we had a poster with thousands of fonts. Admittedly we did not use many of them, but occasionally one of the esoteric ones would be perfect for a job. These fonts, as well as being mathematical curiosities could be used for specific circumstances.

t'aco (-1)

Anonymous Coward | about 6 months ago | (#46787115)

questions, then the resources that bought the farm.... Fact Acame into

Please (3, Insightful)

rossdee (243626) | about 6 months ago | (#46787169)

Monospaced font for numbers, so they can line up in a column

zeroes (3, Insightful)

Anonymous Coward | about 6 months ago | (#46787657)

Monospaced font for numbers, so they can line up in a column

Also: slashed zero, as well as some distinction between capital-i and small-l (el).

A good test string that I ran across was "Illegal1 = O0". Also, m/rn/rri (em/ar-en/ar-ar-eye), w/vv (double-u/vee-vee):

https://en.wikipedia.org/wiki/IDN_homograph_attack

Re:zeroes (1)

Vesvvi (1501135) | about 6 months ago | (#46788097)

I really wish I had mod points for this.

Re:zeroes (0)

Anonymous Coward | about 6 months ago | (#46788697)

I thought about this one a while ago, during an asset register updating that involved writing down many, many, many serial numbers on a notepad for later typing up.

I came up with this:
http://birds-are-nice.me/CANar... [birds-are-nice.me]

Additictive drug for mathematicians (1)

Squidlips (1206004) | about 6 months ago | (#46787369)

Typeface work is an addictive drug for mathematicians. Look at the decade lost by Knuth on this....ugh.

Marain? (0)

Anonymous Coward | about 6 months ago | (#46787401)

http://www.omniglot.com/writing/marain.htm

Re:Marain? (1)

TangoMargarine (1617195) | about 6 months ago | (#46787523)

Looks kind of similar to Aurebesh. [wikia.com] .

Thanks for the link, but...did you have a point?

Re:Marain? (0)

Anonymous Coward | about 6 months ago | (#46787795)

Thought it was interesting to see abstract and mathematically defined typefaces that resolve into a simple binary form - all in fiction defined by computers to unify communication between various intelligent beings.

It resolves nicely in 3x3 form to a strip led system. I use a similar 4x4 type system to increase density of fonts on a tiny display and LED strip display.

Re:Marain? (1)

TangoMargarine (1617195) | about 6 months ago | (#46787895)

I suppose it's a sign of my background when I read about a 9-bit representation and my first thought is that that would work horribly as most platforms these days are based on powers of 2. This is the Culture we're talking about though, heh.

Re:Marain? (0)

Anonymous Coward | about 6 months ago | (#46788765)

Indeed - the wacky, wacky yet appealing Culture...

Another Blog-vertisement (0)

Anonymous Coward | about 6 months ago | (#46788273)

Looks like another blog-vertisement to me.

Meh. (1)

azav (469988) | about 6 months ago | (#46788411)

Why don't people develop new typefaces to represent concepts in programming so we can have better character identifiers for concepts that we need to type out?

Conveyor belt problem... (1)

rgbatduke (1231380) | about 6 months ago | (#46788437)

Interesting article, but I don't understand why the conveyor belt problem (as described) is unsolved. Start with one pulley. Obviously a band around it works. Assume a solution exists for some finite number of pulleys, N. Since the support of the pulley locations is compact, one can always and uniquely determine the exterior of the spanning belt. Place an additional pulley exterior to this belt. There are only three topologically relevant cases -- (an pair of in the case of more than two of) the "nearest neighbor" exterior pulleys carry a belt that is "convex" (outside both), "concave" (inside both), or "mixed" (inside one, outside the other). In all three cases it can be shown that one can add the pulley and still satisfy the conditions of the problem. Hence one has 1, N and N+1, a proof by topological induction. The only additional bit of work on the proof is to note that one can avoid problems with pathological interior loopings (if necessary -- I don't really think that it is) or adding the N+1 pulley INSIDE the belt by simply reordering the inductive process for any given pattern to maintain the belt in a maximally convex state as one proceeds, that is starting with any belt and then adding the pulleys ordered by their distance from the original pulley. Not only is there "a" spanning belt, but there will be in most cases an enormous permutation of spanning belts. As in, all of the permutations one can construct by adding pulleys in circular distance order from any pulley treated as the original pulley until they are all entrained.

Re:Conveyor belt problem... (1)

the phantom (107624) | about 6 months ago | (#46792105)

The paper that they cite is not in English (Abellanas, "Conectando puntos: poligonizaciones y otros problemas relacionados"), so I am not sure that I even really understand what the statement of the problem is. That being said, I don't think that the induction works out the way you want it too. Consider, for example, a situation in which you add a new pulley to an existing configuration and the two nearest neighbors are separated from the pully added by induction by a stretch of conveyor belt that runs between two pulleys that are very far away from the three-pulley configuration under consideration. I don't think that you can actually do the induction on the number of pulleys, as the configuration of the pulleys in addition to the number of pulleys.

Re:Conveyor belt problem... (1)

the phantom (107624) | about 6 months ago | (#46792163)

Man, that second sentence is awkward. I should have edited.

Suppose that there exists a configuration of N pulleys. To this configuration, we add an additional pulley. The two pulleys that are nearest to this new pulley are separated from the new pulley by a segment of conveyor that runs between two additional pulleys that are (potentially) quite distant. This configuration provides a counter example to the induction suggested above.

Re:Conveyor belt problem... (1)

rgbatduke (1231380) | about 6 months ago | (#46799235)

Why? The only issue is the belt convexity. If the new pulley would pull the belt away from the intermediate pulley if it ran on the outside one can simply switch it to the inside. It cannot be pulled away on both sides. The point is that the run of the belt can be made topologically equivalent to a line drawn between all of the pulley centers in the configuration generated by a distance-ordered recursion from any starting point. All one has to prove is that for a trivial set of local geometries, one can always find a side of the pulley that maintains tension upon addition. The diameter of the pulley ends up being functionally irrelevant.

Perhaps I'm not being sufficiently clear. Take a configuration of N points/pulleys presumed to be spanned by a belt that was systematically structured by starting on the pulley closest to the center of the bounding circle. Add one pulley outside or on the bounding circle of the configuration (one can always reorder the problem to ensure that the N+1 pulley is outside or on this bounding circle). Pick the two (most distant from the center, if there are more than two) pulleys that bracket the new pulley inside rays drawn from the center of the circle through the pulley center. One can always loop in the new pulley in between the two thus selected, and one always does so without adding a loop that "occludes" a future distance-ordered addition. The insistence of maintaining rank order and radially ordered convexity as one proceeds suffices to ensure that one can always add a pulley to a suitably developed set of N pulleys.

Or, maybe I'm missing something, but when I draw sequences of points in this way there aren't really a lot of cases to consider on the addition. The convexity requirement eliminates, I think, your assertion of "distant points" for the nearest neighbors. They cannot be more distant than the diameter of the bounding N circle, and the construction ensures that one does not build a loop that twists around in some snaky way across angles. By posing the solution in this way, I simply avoid having to consider going back to do nonlocal rearrangements of some arbitrary looping selected from the (probably quite large) set of loopings that would work for any set of N pulleys. One really only needs to consider the two bracketing pulleys and the two next neighbors of those pulleys with the comfortable constraint that the next nearest neighbor has a belt that run at an angle of pi or less relative to the exterior of the radius of a/the bracketing pulley in question. Four permutations of possible side swap to consider, done, induction proven.

The irony... (1)

cplusplus (782679) | about 6 months ago | (#46789605)

...is that every scalable font is rendered using computational geometry. All curves in characters are defined with three or more points, and your computing device of choice does a lot of math to render pretty little characters for you.

Do any of them (1)

gelfling (6534) | about 6 months ago | (#46790283)

Have to be fucking readable?

wow they suck (0)

Anonymous Coward | about 6 months ago | (#46791555)

I guess it's my own fault for expecting something that didn't make comic sans look classy.

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